6666666666 CAT Questions - Trigonometry, CAT 2017 study material

# CAT Practice : Trigonometry

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## Height of a flag pole

Q.16: A flag is hoisted on top of a building of height 7√3 m. A man of height √3 m,standing on the ground, sees the top and bottom of the flag pole at 2 different angles of elevation that are found to be complementary. If the man is standing √135 m away from the building, find the height of the flag pole.
1. 3√3 m
2. 1.5√3 m
3. 2 / √3 m
4. 6 / √3 m

Choice B. 1.5√3 m

## Detailed Solution

Let height of the flag pole PQ be x
Height of building QR = 7√3 m
Height of man AB = √3
Therefore QQ’ = 7√3 – √3 = 6√3

From diagram, tan y° = QQ’/AQ’
Or tan y° = $\frac{6√3}{√135}$ ------- (1)

Also, tan (90 – y)° = PQ’/AQ’
Or tan (90 – y)° = $\frac{(x + QQ’)}{√135}$
But tan (90 – y)° = cot y°
Therefore cot y = $\frac{x + 6√3}{√135}$
or tan y = $\frac{√135}{x + 6√3}$ --------(2)

Equating (1) and (2), we get
$\frac{6√3}{√135}$ = $\frac{√135}{x + 6√3}$
6√3x + 108 = 135
6√3x = 27
x = 9 / 2√3 or x = 1.5√3

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