If the elevation angle of a camera situated at the top of a pole from a point 20 metre away from the base of the pole is 60 ° , find the height of the pole.

Let the distance between point of observation and foot of tower B C = 20 m Height of tower A B = h Angle of elevation of top of tower θ = 60 ° Now from figure Δ A B C We know that, Δ A B C is a right angle triangle. tan θ = A B B C tan 60 ° = h 20 ⇒ h = 20 3 m . Therefore, height of tower = 20 3 m

If the ratio of the length of a vertical bar to its shadow is 1 : 3 then find the elevation angle of the sun.

Given : Bar Shadow = 1 3 Let, angle of elevation, ∠ A C B = θ Now, tan θ = tan ∠ A C B = A B B C = 1 3 ⇒ tan θ = 1 3 ⇒ tan θ = tan 30 ° ⇒ θ = 30 ° ∴ The angle of elevation = 30 ° .