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A flagstaff stands on a tower. At a point distant 60 m from the base of the tower, the top of the flagstaff makes an angle of $60 °$ and the tower makes an angle of $30 °$ at that very point. What will be the height of the flagstaff?

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69m

68.28m

69.28m

67.8m

answer is C.

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Detailed Solution

Given,
BC= 60 m
Flagstaff makes an angle=

60 °

The tower makes an angle =

30 °

We use the trigonometric identity

tan θ = p e r p e n d i c u l a r b a s e

.
We draw diagram,
Question Image

We get the value of AB from

Δ A B C

tan 60 ° = A B B C ⇒ 3 = A B 60 ⇒ A B = 60 × 3 [∵ tan 60 ° = 3] ⇒ A B = 103.92

We get the value of DB from

Δ D B C

tan 30 ° = D B B C ⇒ 13 = D B 60 [∵ tan 30 ° = 13] ⇒ D B = 60 × 13 ⇒ D B = 34.64

We get the height of flagstaff,

A D = A B − B D ⇒ A D = 103.92 − 34.64 ⇒ A D = 69.28 m

Thus the height of Flagstaff will be

m.
Therefore the correct option is 3.

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