Question

From the top of a building 15m high the angle of elevation of the top of a tower is found to be 30degree From the bottom of the same building, the angle of elevation of the top of the tower and the distance between the tower and building​

Answer 1

Answer:

Height =  22.5 m

Distance =  7.5√3 m

Step-by-step explanation:

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

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