The shadow of a tower standing on the level ground is found to be 40 m

longer when the sun’s altitude is 30 than when it is 60 Find the height

of the tower.

Question

The shadow of a tower standing on the level ground is
found to be 40 m
longer when the sun’s altitude is
30  than when it is
60  Find the height

of the tower

Anne Simmi · Accepted Answer

let the height of the tower be AB = h m let BC and BD be the length of the shadow such that CD = 40 m in the triangle ABC, $\tan 60 = \frac{A B}{B C} \sqrt{3} = \frac{h}{B C} B C = \frac{h}{\sqrt{3}} m (1)$ in the triangle ABD, $\tan 30 = \frac{A B}{B D} \frac{1}{\sqrt{3}} = \frac{h}{B D} B D = \sqrt{3} h m (2)$ since BD= BC+CD $\sqrt{3} h = \frac{h}{\sqrt{3}} + 40 3 h = h + 40 \sqrt{3} 2 h = 40 \sqrt{3} h = 20 \sqrt{3} m$ thus the height of the tower is $20 \sqrt{3} m$ hope this helps you

The shadow of a tower standing on the level ground is found to be 40 m longer when the sun’s altitude is 30 than when it is 60 Find the height of the tower.

The shadow of a tower standing on the level ground is found to be 40 m

longer when the sun’s altitude is 30 than when it is 60 Find the height

of the tower.