Question

The angle of elevation of the top of a tower from the foot of the building is 30° and the angle of elevation of the top of the building from the foot of the top of the tower is 60°. What is the ratio of heights of tower and building.

Answer 1

Answer:

AB = Height of tower (h1)

CD = Height of building (h2)

BC = distance between tower and building (x)

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In ∆ ABC,

Tan 30 = AB/ BC

1/√3 = h1/x

x = √3 (h1) .....(1)

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In ∆ BCD ,

Tan 60 = CD/BC

√3 = h2 / x

x = h2/√3. ......(2)

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COMPARE EQ. (1) AND EQ. (2),

√3h1 = h2/√3

3h1 = h2

h1/h2 = 1/3

So,

Ratio of height of tower and Height of building is 1:3.

Step-by-step explanation: