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A person stands 36 metres away from the foot of a tower. The angle of elevation to the top of the tower is θ, and tanθ = 5/3. What is the height (in m
Question

A person stands 36 metres away from the foot of a tower. The angle of elevation to the top of the tower is θ, and tanθ = 5/3. What is the height (in metres) of the tower?

A.

45

B.

60

C.

54

D.

48

Correct option is B

Given
Distance from the foot of the tower (Base) = 36 m
tanθ=53\tan \theta = \frac{5}{3}​​
Formula Used
tanθ=Perpendicular (Height of tower)Base\tan \theta = \frac{\text{Perpendicular (Height of tower)}}{\text{Base}}​​
Solution
Let the height of the tower be h.
h36=53 h=36×53 h=12×5=60m \frac{h}{36} = \frac{5}{3} \\\ \\h = 36 × \frac{5}{3} \\\ \\h = 12 × 5 = 60 m \\\ \\​​
Final Answer
So the correct answer is (b)

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