Math, asked by mnmshajahan125, 1 year ago

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.

Answers

Answered by delealifan
33

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Answered by athleticregina
13

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}

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