From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower - Maths - Some Applications of Trigonometry

Question

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 45Â° and 60Â° respectively
Find the height of the tower

Mayank Bhardwaj · Accepted Answer

Dear Student! Here is the answer to your query

Let AB and BC be the transmission tower and Building and D be the point of observation Given BC = 20 metres Let AB = h metres Now âˆ BDC = 45Â° and âˆ ADC = 60Â° In Î”BDC $\tan 45 ° = \frac{BC}{DC} \Rightarrow 1 = \frac{20}{DC}$ â‡’ DC = 20 m Now in Î”ADC $\tan 60 ° = \frac{AC}{DC} = \frac{AB+BC}{DC} \Rightarrow \sqrt{3} = \frac{h + 20}{20} \Rightarrow 20 \sqrt{3} = h + 20 \Rightarrow h = 20 \sqrt{3} - 20 = 20 (\sqrt{3} - 1)$ âˆ´ The height of the tower is 20 $(\sqrt{3} - 1)$ metres Cheers!

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