Question

A shadow of the tower standing on a level of ground is found to be 40m longer when the sun's attitude is 30° than when it is 60°. Find the height of the tower​

Answer 1

Step-by-step explanation:

Let's take height of tower as X.

$\tan(30) = \frac{40}{x} \\ \frac{1}{ \sqrt{3} } = \frac{40}{x} \\ x = 40 \sqrt{3}$

Lets take shadow of tower as Y.

$\tan(60) = \frac{40}{x + y} \\ \sqrt{3} = \frac{40}{40 \sqrt{3} + y } \\ 120 + \sqrt{3} y = 40 \\ \sqrt{3} y = 40 - 120 \\ y = \frac{ - 80}{ \sqrt{3} }$

We took X and Y as the height and shadow of the tower

So X + Y= tower

$40 \sqrt{3} - \frac{80}{ \sqrt{3} } \\ \frac{120 - 80}{ \sqrt{3} } \\ \frac{40}{ \sqrt{3} }$

This the answer for this question.

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