Question

find out the angle of depression made by a man, who observes a point on the ground from the top of a building 50m high and the length from the top of the building to the point is 100m.

Answer 1

Required Answer:-

Along the line of sight, The angle of depression becomes equals to angle of elevation of the top of building from a point.

Here we have:

• Height of the building (p) = 50 m
• Distance from point to top (h) = 100 m

We need to find the angle of elevation. Since the measures of perpendicular and hypotenuse is known, we can use sine for determining θ.

➛ sin θ = p/h

➛ sin θ = 50 m / 100 m

➛ sin θ = 1/2

In trigonometry, Sin θ is equals to 1/2 when θ = 30°. Hence, the angle of depression = angle of elevation of the point is 30° (Ans)

Trigonometric table:-

$\bullet\:\sf Trigonometric\:Values :\\\\\boxed{\begin{tabular}{c|c|c|c|c|c}Radians/Angle & 0 & 30 & 45 & 60 & 90\\\cline{1-6}Sin \theta & 0 & \dfrac{1}{2} & \dfrac{1}{\sqrt{2}} & \dfrac{\sqrt{3}}{2} & 1\\\cline{1-6}Cos \theta & 1 & \dfrac{\sqrt{3}}{2}& \dfrac{1}{\sqrt{2}}& \dfrac{1}{2}&0\\\cline{1-6}Tan \theta&0& \dfrac{1}{\sqrt{3}}&1&\sqrt{3}&Not D{e}fined\end{tabular}}$