From the top of a building 15m high

Asked by admin @ 29/08/2021 in Math viewed by 278 People

From the top of a building 15m high the angle of elevation of top of a tower is 30 degree..from bottom of same building ,angle of elevation of same building is 60 degree..find height of tower and distance b/w tower and building

Answered by admin @ 29/08/2021

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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