The length of the shadow of a tree is 18 metres, when the sun is at an elevation of 40°. What is the height of the tree?

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Solution

Let AB be the height of the tree and BC be the length of the shadow.

Given: BC = 18 m and ∠ACB = 40°

In ΔABC, ∠ABC = 90°

⇒ AB = BC × tan 40°

⇒ AB ≈ 18 × 0.8391 cm

= 15.1038 m

Therefore, the height of the tree is approximately 15.10 m.

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What is the angle of elevation of the sun, 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 the shadow of a tree is 18 metres, when the sun is at an elevation of 40°. What is the height of the tree?

Let AB be the height of the tree and BC be the length of the shadow. Given: BC = 18 m and ∠ACB = 40° In ΔABC, ∠ABC = 90° ⇒ AB = BC × tan 40° ⇒ AB ≈ 18 × 0.8391 cm = 15.1038 m Therefore, the height of the tree is approximately 15.10 m.

Let AB be the height of the tree and BC be the length of the shadow.

Given: BC = 18 m and ∠ACB = 40°

In ΔABC, ∠ABC = 90°

⇒ AB = BC × tan 40°

⇒ AB ≈ 18 × 0.8391 cm

= 15.1038 m

Therefore, the height of the tree is approximately 15.10 m.