A man observes that when he moves up a distance c metres on a slope, the angle of depression of - Maths - Coordinate Geometry

Question

A man observes that when he moves up a distance c metres on a
slope, the angle of depression of a point on the horizontal plane
from the base of the slope is 30°, and when he moves up further
a distance c metres, the angle of depression of that point is
45° The angle of inclination of the slope with the horizontal
is:-

Mayank Jha · Accepted Answer

Dear student,

Figure to represent the given information will be:

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_57f5c3bec09d3%20jpg"
style="width: 206px; height: 123px;">
Applying m - n theorem of trigonometry, we get:(c + c) cot(Θ - 30°) = c cot 15° - c cot 30°⇒cot(Θ - 30°) = 12sin(30° - 15°)sin 15° sin 30°⇒cot(Θ - 30°) = 121sin 30° = 1 = cot 45°⇒Θ - 30° = 45°∴Θ = 75°

So, angle of inclination if the slope with horizontal will be
75°

Regards