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An observer 1.5 m tall is 28.5 m away from a tower. The angle

Question

An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his/her eyes has measure 45. What is the height of the tower?

A

28.5 m

B

30 m

C

27 m

D

1.5 m

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An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his/her eyes has measure 45. What is the height of the tower?

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Text solutionVerified

We can form the above figure by given data

⟹ B D = CE = 1.5

In

Δ A BC, ∠ CB A = 9 0^{o}

⟹ tan 4 5^{o} = \frac{A B}{BC}

⟹ 1 = \frac{A B}{28.5}

⟹ A B = 28.5

Now,

h = A B + B D = 28.5 + 1.5 = 30

Hence, height of the tower is

30 m

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Question Text	An observer 1.5 m tall is 28.5 m away from a tower. The angle of elevation of the top of the tower from his/her eyes has measure 45. What is the height of the tower?
Answer Type	Text solution:1
Upvotes	150