Find the length of the shadow cast by a tree $60 m$ high when the sun’s altitude is $30^{\circ}$ .

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Solution

Step: Finding the length of the shadow .
Let us assume that $P Q$ be the tree of height $60$ m and $Q R$ be its shadow.
Then,

In $△ P Q R$ ,
$tan 30^{\circ} = \frac{P Q}{Q R}$
$\frac{1}{\sqrt{3}} = \frac{60}{Q R}$
$Q R = 60 \sqrt{3} m$
Therefore, length of the shadow is $60 \sqrt{3} m$ .

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Angle of Elevation

Standard X Mathematics

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Find the length of the shadow cast by a tree 60 m high when the sun’s altitude is 30∘.

Step: Finding the length of the shadow . Let us assume that PQ be the tree of height 60 m and QR be its shadow. Then, In △PQR, tan30∘=PQQR 1√3=60QR QR=60√3 m Therefore, length of the shadow is 60√3 m.

Find the length of the shadow cast by a tree $60 m$ high when the sun’s altitude is $30^{\circ}$ .

Step: Finding the length of the shadow .
Let us assume that $P Q$ be the tree of height $60$ m and $Q R$ be its shadow.
Then,

In $△ P Q R$ ,
$tan 30^{\circ} = \frac{P Q}{Q R}$
$\frac{1}{\sqrt{3}} = \frac{60}{Q R}$
$Q R = 60 \sqrt{3} m$
Therefore, length of the shadow is $60 \sqrt{3} m$ .