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A flagstaff stands on a vertical tower. At a point distance 10 m from the base of the tower, the tower and the flagstaff make angles 45 and 15 respectively. What will be the length of the flagstaff?

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6.33m

7.33m

7.35m

6.35m

answer is B.

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Detailed Solution

Given,
Distance from the base of the tower =

10

m
The angles made by tower and flagstaff respectively are 45 and 15.
We draw the diagram,
Question Image

We have

B C = 10

m,
Using the identity

tan θ = Perpendicular Base

Δ A B C

tan θ = AB BC

Substituting BC=10, and

θ

45 °

in the equation

tan θ = AB BC

⇒ tan 45 ° = A B 10 ⇒ A B = 10 tan 45 ° ⇒ A B = 10 m [∵ tan 45 ° = 1]

Using the identity

tan θ = Perpendicular Base

Δ D B C

tan α = DB BC

Substituting BC=10, and

α

15 °

⇒ tan 15 ° = D B 10 ⇒ D B = 10 tan 15 ° ⇒ D B = 2.67 m [∵ tan 15 ° = 0.267]

The length of the flagstaff will be,

A D = A B − D B ⇒ A D = 10 − 2.67 ⇒ A D = 7.33 m

Thus the length of the flagstaff will be

7.33

m.
Therefore the correct option is 2.

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