Question

a pole 10m high casts a shadow 10√3m on ground then find sun's elevation

Answer 1

θ=30°.
∵
tanθ=opp/adj=10/10√3=1/√3
tanθ=1/√3
∵ tan 30°=1 / √3,
∴θ=30°

Answer 2

Sun’s elevation angle is 30 degree when a pole is of height 10 m high and shadow is at $10 \sqrt{3}\ m$.

Solution:

Height of pole = 10m

Length of shadow casted on ground =  $10 \sqrt{3}\ m$  

Height of triangle is shown in below attached picture.

Angle A is extended and elevation angle of sun is

$\tan A=\frac{10}{10 \sqrt{3}}=\frac{1}{\sqrt{3}}$

Now value of A = $\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$= 30 degree.

Angle elevation of the sun is 30 degree.