Question

From a top of a building 15m high the angle of elevation of the top of a tower is found to be 30° from the bottom of same building the angle of elevation of the top of tower is found to be 45° determine the height of tower and distance between them. With Diagram

Answer 1

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Answer:

Height =  22.5 m

Distance =  7.5√3 m

Step-by-step explanation:

Define x:

Let x be the difference in the height of the two building.

Let y be the distance between the two building

Form the first equation:

tan θ = opp/adj

tan(30) = x/y

y tan (30) = x

y = x/tan(30)

y = 3x/√3

Form the second equation:

tan θ = opp/adj

tan(60) = (15 + x)/y

y tan(60) = 15 + x

y = (15 + x)/tan(60)

y = (15 + x)/√3

Equate both y:

3x/√3 =  (15 + x)/√3

3x = 15 - x

2x = 15

x = 7.5 m

Find y:

y = 3x/√3

y = 3(7.5)/√3

y = 7.5√3 m

Height of the tower = x + 15 = 7.5 + 15 = 22.5 m

Distance between the two building = y = 7.5√3 m

Answer: Height =  22.5 m, Distance =  7.5√3 m

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