Question

The shadow of a tower standing on a level ground is found to be 20m longer when the sun's altitude is 45° than when it is 60°. Find the length of the tower. ​

Answer 1

Answer:

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Answer 2

The value of length of the tower is h = 47.32 m

Step-by-step explanation:

From the figure h = length of the tower

From the Δ ABC

$\tan 60 = \frac{h}{x}$

⇒ h = 1.732 x ------- (1)

From the Δ ABD

$\tan 45 = \frac{h}{20 + x}$

⇒ h = 20 + x ------ (2)

Equating equation (1) = equation (2)

1.732 x = x + 20

⇒ 0.732 x = 20

⇒ x = 27.32 m

Thus the height of the tower is given by

h = 1.732 x

⇒ h = 1.732 × 27.32

⇒ h = 47.32 m

This is the value of height of the tower.