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Syllabus

The angle of elevation of a jet plane from a point A on the ground is 60

^{0.}After a flight of 15 sec,the angle of elevation changes to 30^{0}.If the jet plane is flying at a height of 1500 root 3 m,find the speed of the jet plane.Find the cosine of the angle swept by the minute hand of a clock in 20 minutes.

From the top of the building 60m high the angle of depression of the top and bottom of a vertical lamp post are observed to be 30 degree and 60 degree respectively find

a)the distance between the building and the lamp post

b)the height of the lamp post

are 60

^{o} and 30^{o} respectively. Find the vertical distance between the two planes.The angle of elevation of a jet fighter from point A on the ground is 60°.After a flight of 15 seconds, the angle of elevation changes to 30°.If the jet is flying at a speed of 720 km/h, find the constant height at which jet is flying.

If the angle of elevation of a cloud from a point

hmetres above a lake isalphaand the angle of depression of its reflection isbeta. Prove that the height of cloud ish(tan beta + tan alpha)/ tan beta - tan alphaa tower casts a shadow 90 m long and at the same time another tower casts a shadow of 120 m on the ground. if the height of the second tower is 80 m, then what is the height of the first tower?

The angle of elevation of a cloud from a point 60m above the lake is 30 and the angle of depression of its reflection in the lake is 60.find the height of the cloud above the lake?

A man standing on the deck of a ship, which is 10m above the water level, observes the angle of elevation of the top of a hill as 60 degree and the angle of depression of the base of the hill as 30 degree. Find the distance of the hill fom the ship and the height of the hill.

attached to her telescope, she fi nds the angle of depression to the bottom of this tree is 30?, while the angle of elevation to the

top of the tree is 60?. The angle of elevation to the troop of baboons is 45?. Use this information to fi nd (a) the height of the

observation post, (b) the height of the baboons? tree, and (c) the height of the baboons above ground.

The Angle of elevation of th top of a vertical tower from a point on the ground is 60

^{o.}From another point 10m vertically above the first, its angle of elevation is 30^{o.}Find the height of tower? ...................Please provide me answer as soon as possible....how to solve this to get 200/root 3?

x(root 3+1)=200(root 3+1/root 3)

The angle of elevation of the top Q of a vertical tower PQ from point X on the ground is 60 degree.At a point Y 40m vertically above X the angle of elevation is 45 degree .Find the height Of the tower PQ and distance XQ.

the angles of depression of the top and bottom of an 8m tall building from the top and bottom of a multistoreyed buildin are 30 and 45 degrees respectively. find the height of the multistoreyed building and the distance between the twoo buildings. please anser me fast today is my test.

WITHOUT USING TRIGONOMETRIC TABLE,PROVE-

sin 5 tan 22 sec 60 tan 68 sec 85 = 2

the angles of elevation of the top of a tower from two points at a distance of 4m and 9m from the base of the tower and in the same straight line with it are complementary. prove that the height of the tower is 6 m

the length of the string between a kite and a point on the ground is 90m . the string makes an angle of 60 degrees with the level ground . assuming that their is no slack in the string find the height of the kite

A boy standing on a horizontal plane finds a bird flying at a distance of 100m from

him at an elevation of 30

0. A girl standing on the roof of 20 meter high building finds the angle of elevation of the same bird to be 450. Both the boy and the girl are on opposite sides of the bird. Find the distance of the bird from the girl.

Q.There are two temples, one on each bank of a river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top &the foot of the other temple are 30^{0}& 60^{0}respectively. Find the width of the river and the hight of the other temple.From the top of a hill the angle of depression of the two consecutive kilometre stones due to east are found to be 30

^{o}and 45^{o}.Find the height of a hill.FROM THE TOP OF A TOWER 50M HIGH THE ANGLES OF DEPRESSION OF THE TOP AND THE BOTTOM OF A POLE ARE OBSERVED TO BE 45DEGREE AND 60DEGREE RESPECTIVELY. FIND THE HEIGHT OF THE TOWER

(1/sec

^{2}A-cos^{2}A + 1/cosec^{2}A-sin^{2}A) (sin^{2}Acos^{2}A) = 1-sin^{2}Acos^{2}A/2+sin^{2}Acos^{2}AIn a flight of 600 km , an aircraft was slowed down due to bad weather. The average speed for the trip was decreased by 200 km/h & the time of flight increased by 30 minutes. Find the duration of flight.

a ladder rests against a vertical wall at an inclination of

to the horizontal.its foot is pulled away from the wall through a distancealphapso that its upper end slides a distanceqdown the wall and then the ladder makes an angle ofbetato the horizontal show thatp/q= cos beta - cos alpha/ sin alpha -sin betaa bird sitting on the top of a tree, which is 80m high. the angle of elevation of the bird, from the point on the ground is 45

^{0}. the bird flies away from the point of observation horizantally and remains at a constant height. after 2 seconds, the angle of elevation of the bird from the point of observation becomes 30^{0}. find the sped of the flying birdFrom a top of a 7m high building, the angle of elevation of the top of a cable tower is 60 degree & the angle of depression of its foot is 45 degree. Determine the height of the tower.

PLZ ANSWER IN UNDERROOTS & WITH THE FIGURE.

as observed from the top of a lighthouse 100m above sea level the angle of depression of a ship sailing directly towards it changes from 30 degree to 60 degree. determine the distance travelled by the ship during the period of observation

The elevation of a hill from a point P due east of it is θ and at a place Q due south of P, the elevation is φ. If the distance PQ be d, find the height of the hill.

a pole 6 m high casts a shadow 2 root 3 m on the ground then the sun's elevation is :

a-60 degrees

b-45 degrees

c - 30 degrees

d-90 degrees

from a window 60m high above the ground of a house in a street the angles of elevation and depression of the top and foot of another house on the opposite side of the streer are 60degree and 45degree respectively. show that the height of th opposite house is 60(1+ root3)

An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60V. After a flight of 10 seconds, its angle of elevation is observed to be 30V from the same point on the ground. Find the speed of the aeroplane in km/hour.

a path separates two walls .A ladder leaning against one wall rests at apoint on the path .It reaches a height of 90m on the wall and maks and makes an angle of 60 degree with the ground . If while resting at the same point on the path , it is made to lean against the other wall , it would have made an agle of 45 degree with the ground. find the height it would have reached on the second wall.

At the foot of a mountain the elevation of its summit is 45° . After ascending 1000m

^{0}and the angle of depression of its reflection in the lake is 60^{0}. Find the distance of the bird from the point of observation.16)the angle of elevation of the top of a tower from a point A on the ground is 30 degree.on moving a distance of 20metres towards the foot of the tower to a point B the angle of elevation increases to 60 degree.find the height o the tower and the distance of the tower from the point A.

observed that the angle of elevation of the top of the

tower changed to 60

^{0}from 45^{0}. How much more thanwill he take to reach of the tower?

(a) 5 min

(c) $5\left(\sqrt{3}-1\right)$min

(b) 5$\sqrt{3}$ min

(d) None of these

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car as an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

The length of the shadow of a tower standing on level ground is found to be 2x metres longer

when the sun’s altitude is 30° than when it was 45°. Prove that the height of tower is (√3+1)x

metres.

A man on the top of a vertical observation building observes a truck moving at a

uniform speed coming directly towards it. If it takes 18 minutes for the angle of

depression to change from 30° to 60° how soon after this will the truck reach the

observation building?

A fire in building B is reported on telephone to two fire stations P and Q, 20 km apart from each other on a straight road. P observes that the fire is at an angle of 60 degree to the road and Q observes it an angle of 45 degrees to the road.Which station should send its team and how much will the team have to travel ?

The shadow of a vertical tower on level ground increases by 16 m when the altitude of the sun changes from angle of elevation 60 degree to 45 degree.Find the height of the tower,correct to one place of decimal.(Take root 3=1.73)

an aeroplane at an altitude of 200m the angle of depression of two opposite pointso two banks of a river to be 45 and 60 degrees. find the width of the river in meters

1. If 3cotA= 4 ,check whether

1- tan= cos^{2}A^{2}A – sin^{2}A or not1+ tan

^{2}A2. If tanA= a/b, find the value of

cosA + sinAcosA – sinA

3. If 3 tanA = 4, find the value of

4cosA – sinA2cosA + sinA

4. If 3cotA = 2, find the value of

4sinA – 3cosA2sinA + 6cosA

5. If tanA = a/b, prove that

asinA – bcosA=a^{2}– b^{2}asinA + bcosA a

^{2}+ b^{2}6. If secA = 13/5, show that

2sinA – 3cosA= 34sinA – 9cosA

7. If cosA = 12/13, show that sinA(1 - tanA)= 35/156

From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower

A straight highway leads to the foot of a tower .A man standing at the top of the tower

A fire in the building B is reported on telephone to two fire stations P and Q, 20km apart from each other on a straight road. P observes that the fire is at the angle of 60° to the road and Q observes that it is at an angle of 45° to the road. Which station should send its team and how much will this team have to travel?

Two poles of equal heights are standing opposite each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60 digree and 30 digree, respectively. Find the height of the poles and the distance of the point from the poles.

9) a vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres.at a point on the plane,the angles of elevation of the bottom and the top of the flag-staff are respectively 30 degree and 60 degree.find the height of the tower.

1) the difference between the heights of the lighthouse and the building

2) the distance between the light house and the building

the tops of two poles of height 16m and 10m are connected by a wire . If the wire makes an angle of 30 with the horizontal , then the length of the wire ... ??Two ships are sailing on the sea on either side of the lighthouse.The angle of the depression of the ship as observed from the lighthouse are 60

^{o}and 45^{o}respectively.If the distance between the ship is 200(root 3 +1)/root 3 metre,find the height of the lighthouse.From a point 100m above a lake the angle of elevation of a 30 degree and angle of depression of its reflecting in the lake is 60 degree. find the height of helicopter.

at a point on a level plane, a tower subtends an angle alpha and a man, a meters tall standing on its top, subtends an angle beta. prove that the height of the tower is acot(alpha+beta)/cot alpha - cot (alpha+beta)

A man on a deck of a ship 12m above water level observes the angle of elevation of the top pf a cliff is 60degree and the angle of depression of the base of the cliff is 30degree. Find the distance of the cliff from the ship and the height if the cliff .the angles of depression of two ships from the top of a light house are 45 and 30 towards east.if the ship some 100 m apart find the height of light house?

Two boats approach a light house in mid-sea from opposite directions.The Angles of elevation of the top of the light house from two boats are 60 and 45 respectively.If the distance between the two boats is 100m,find the height of hte light house.

Q. (Cosec A - Sin A) (Sec A - Cos A)= 1/(Tan A + Cot A)

Prove LHS = RHS

A tree 12m high, is broken by the wind in such a way that its top touches the ground and makes an angle of 60degree with the ground .. At what height from the bottom, the is broken by the wind???angle of elevation of the top of the hill at the foot of tower is 60 degrees and the angle of elevation of tower from the foot of the hill is 30 degrees. if tower is 50m high find the height of hill

the angle of elevation of a jet fighter from a point A on the ground is 60 degree .after a flight of 15 seconds , the angle of elevation changes to 30 degree . if the jet is flying the speed of 720km/h . find the height at which jet is flying ? [root3=1.732]

A man on cliff observes a boat at an angle of depression of 30 degree which is approaching the shore to the point immediately beneath the observer with a uniform speed. Six minutes later , the angle of depression of the boat is found to be 60 degree . Find the total time taken by the boat to reach the shore .

the angle of an aeroplane friom a point on the ground is 45 degree. After flight for 15 sec. the elevation changess to 30 degree. If the aeroplane is flying at the heighht odf 3000 m .Find the speed of the aeroplane ?

A 1.6m tall, girl stands ata distance of 3.2m from a lamp-post and cats a shadow of 4.8m on the grond. Find the height of the lamp-post by using (i)trignometric ratios (ii)property of similiar triangles.

how does 87/root3 becum 29root3????

A round balloon of radius r subtends an angle α at the eye of the

An aeroplane flying horizontally 1 km above the ground is observed at an angle of elevation of 60 degree from a point on the ground. If after 10 seconds, the angle of elevation is observed to be 30 degree, find the uniform speed of the aeroplane in km/hr

At a point on level ground, the angle of elevation of a vertical tower is found such that it's tangent is 5/12 . On walking 19.2 mtrs towards the tower , the tangent of the angle of elevation is 3/4 . Find height of the tower?????

Q. If $\mathrm{sin}\theta =\frac{m}{n}$, find the value of $\frac{\mathrm{tan}\theta +4}{4cot\theta +1}$

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

An aeroplane flying horizontally at a height of 2500m above the ground is observed at a certain point on earth to subtend and angle of 60

^{0}. After 15 seconds, its angle of elevation at the same point is observed to be 30^{0}. Calculate the speed of the aeroplane.Find the distance of the point from the top of the tower .

Experts answer fast

The shadow of a tower standing on the level ground is found to be 40 m

longer when the sun’s altitude is 30 than when it is 60Find the height

of the tower.

From a window 15m high above the ground in a street ,the angles of elevation and depression of the top and foot of another house on the oppositeside of the street are 30

^{0}and 45^{0}.show that the height of the opposite houde is 23.66mFind the angular elevation of the Sun when the shadow of a 10m long pole is 10√3m.

the angle of elevation of an aeroplane from a point on the ground is 45 degree. After 15 seconds of flight the angle changes to 30 degree.f the plane is flying at a constant height of 2500m,find the speed of the plane.

1. the same side of the tower

2. the opp. sides of the tower

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IF A PERSON ONWALKING 20 M TOWARDS CHIMNEY IN A HORIZONTAL LINE THROUGH ITS BASE OBSERVES THAT ITS ANGLE OF ELEVATION CHANGES FRO 30 TO 456 THEN THE HEIGHT OF CHIMNEY???

A tree breaks due to storm and the broken part bends, so that the top of the tree touches the ground making an angle of 30 degree with the ground. The distance between the foot of the tree to the point where the top touches the ground is 8m find he height of the tree.

a man standing on deck of ship which is 10m above the sea level, observes the angle of elevation of the top of a cloud as 30 degree and angle of depression of its reflection in the sea was found to be 60 degree. find the height of the cloud and also the distance of cloud from the ship

Among two towersTandR, if the height ofTis 72 m, which is less than that ofR, the angle of depression of the top ofTfrom the top ofRis 30° and its angle of elevation from the foot ofRis 45°, then height ofRis