Question

the shadow of a vertical tower on level ground increase my 16m when the altitude of the sun changes from angle of elevation 60degree to 45degree. Find the hight of the tower, correct to one place of decimal

Answer 1

is it right or wrong

Answer 2

Answer: The height of tower  is 37.85 m².

Step-by-step explanation:

Since we have given that

First angle of elevation to form the shadow of a vertical tower = 60

Second angle of elevation to form the shadow of a vertical tower = 45

The shadow of a tower on level ground increases by 16 m when the altitude of the sun changes from 60° to 45°.

As shown in the figure below:

As we need to find the height of the tower:

$h=\frac{d}{\cot x-\cot y}\\\\h=\frac{16}{\cot 60^\circ-\cot 45^\circ}\\\\h=\frac{16}{1-\frac{1}\sqrt{3}}}\\\\h=\frac{16\sqrt{3}}{\sqrt{3}-1}\\\\h=\frac{16\sqrt{3}}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}\\\\h=8\times \sqrt{3}(\sqrt{3}+1)\\\\h=37.85\ m$

Hence, the height of tower  is 37.85 m².