When the sun is at an elevation of 60 the length of the shadow of a tree is 15 Metres What is the height of the tree?

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Find the length of the shadow cast by a tree 60 m high when the sun's altitude is `30^circ`.

Let AB be the tree of height 60 m and BC be its shadow .

In ΔABC

`"AB"/"BC"` = `tan30^circ`

`60/"BC" = 1/sqrt(3)`

`"BC" = 60sqrt(3)` m

So , height of tower is `60sqrt(3)` m .

Concept: Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables

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Answer

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Hint: The Angle of elevation is the angle formed from the ground to the Top point of the object. Using the trigonometric value of that angle, we can use it to find the height of the object in this condition, where we have the length of the shadow.

Complete step-by-step answer:

Let’s begin with the given information of having the shadow length 16 m which is the distance between the tree bottom to the tip of the shadow. Another information is that the angle of elevation is 60$^ \circ $ which is inclined between the ground and the line between top of tree to ground.

According to the figure, we get that \[\ \tan {60^ \circ }\, = \,\dfrac{h}{{16}} \\ h = \,16\,\tan {60^ \circ } \\ = \,16\,\sqrt 3 \\ \] Thus, the height of the tree is $16 \sqrt 3 $ m. Option c is the correct option.Note: Angle of elevation is the angle formed by real line to the ground and angle of depression is angle formed while looking diagonally down to the horizon of the sky. Don’t confuse between the angle of elevation and angle of Deviation.