The length of shadow of a tree is $16 m$ when the angle of elevation of the sun is $60^{\circ}$ . What is the height of the tree?

8

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16

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16 \sqrt{3}

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\frac{16}{\sqrt{3}}

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Solution

The correct option is C $16 \sqrt{3}$ m
Let $A B = h$ be height of the tree and $B C$ be it's shadow.
In $△ A B C$
$\frac{h}{16} = tan 60^{o}$
$h = tan 60^{0} \times 16$
$h = 16 \sqrt{3}$
$∴$ Height of the tree is $16 \sqrt{3} m$

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Q. If a tree of height 12 m casts a shadow of 30 m, then a tree of height 16 m will cast a shadow of .

Q. The angle of elevation of the sun is , when the length of the shadow of a tree is equal to the height of the tree.

When the sun is at an elevation of $35^{\circ}$ , the shadow of a tree is 10 m. What would be the length of the shadow, when the sun is at an elevation of $25^{\circ}$ ?

$[\begin{matrix} T a n 25^{\circ} = 0.46 T a n 35^{\circ} = 0.7 \end{matrix}]$

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The length of shadow of a tree is 16 m when the angle of elevation of the sun is 60∘. What is the height of the tree?

The correct option is C 16√3 mLet AB=h be height of the tree and BC be it's shadow.In △ABCh16=tan60o h=tan600×16 h=16√3∴ Height of the tree is 16√3 m

The length of shadow of a tree is $16 m$ when the angle of elevation of the sun is $60^{\circ}$ . What is the height of the tree?

The correct option is C $16 \sqrt{3}$ m
Let $A B = h$ be height of the tree and $B C$ be it's shadow.
In $△ A B C$
$\frac{h}{16} = tan 60^{o}$
$h = tan 60^{0} \times 16$
$h = 16 \sqrt{3}$
$∴$ Height of the tree is $16 \sqrt{3} m$