Question

Find the angle of elevation of the sun when the length of the shadow of a tree is √3 times the height of the tree.

Answer 1

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Answer 2

Answer:

$\theta=30^{\circ}$

Step-by-step explanation:

Let AB be the tree and AC be its shadow,

Then, the shadow of a tree is √3 times the height of the tree.

Let height of tree be h then height of shadow will be √3h

Lets assume h be the height of the tree.

Using trigonometric ratio,

$\tan\theta=\frac{Perpendicular}{base}$

We have to find the angle of elevation of the sun that is $\theta$

perpendicular = AB and base = AC

Substitute, we get,

$\tan\theta=\frac{AB}{AC}$

$\tan\theta=\frac{h}{\sqrt{3}h}$

simplify, we get,

$\tan\theta=\frac{1}{\sqrt{3}}$

we know  $\tan30^{\circ}=\frac{1}{\sqrt{3}}$

Thus $\theta=30^{\circ}$