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Q.

The angle of elevation of the tip of a flag staff from a point 10 meter due south of its base is $60 °$ . Then the height of the flag staff will be_____ .

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a

15 m

b

16 m

c

17 m

d

18 m

answer is C.

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Detailed Solution

seo

Let A, B, C be the tip of the flag staff, ground and base of the flag staff respectively.
We are given that the angle of elevation of the tip of a flag staff is

60 °

and the distance between the base of the flag staff and the ground is 10 m.
We know that the side opposite to the right angle is called the hypotenuse, the side opposite to the given angle is called the opposite side, the side which is next to the given angle and is not hypotenuse is called the adjacent side.
From the diagram, we know that θ =

60 °

, BC = 10 m θ and AC = h
So, the trigonometric ratio defining a relation between opposite side and adjacent side is the tangent.
In a right angled triangle, ΔABC
By using trigonometric ratio, we get

tan θ = Opposite side Adjacent side ⇒ tan θ = A C B C

Substituting

θ = 60 °, B C = 10 m

and

A C = h

in the above equation, we get

⇒ tan 60 ° = h 10

We know that the trigonometric value of

tan 60 ° = 3

. So, Substituting

tan 60 ° = 3

in the above equation, we get

⇒ 3 = h 10

On cross multiplication, we get

⇒ h = 3 × 10 ⇒ h = 1.732 × 10

By multiplying the terms, we get

⇒ h = 17.32 m ⇒ h ≈ 17 m

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