Question

A person observed the angle of elevation of a tower a 45°. He walked 100m towards the foot of the tower and the elevation angle is found to be 60°. Find the height of the tower.

Answer 1

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Answer 2

Answer:

236.6 m

Step-by-step explanation:

Define x and y:

Let the height of the tower be x.

Let the distance from the first observation point to the tower be y

At the first observation point:

tan θ = opp/adj

tan (45) = x/y

x = y tan (45)

x = y ------------- [ 1 ]

At the second observation point:

tan θ = opp/adj

tan (60) = x/(y - 100)

x = (y - 100) tan (60) ------------- [ 2 ]

Solve y :

Sub [ 1 ] into [ 2 ] :

y = (y - 100) tan (60)

y = y tan (60) - 100 tan (60)

y tan (60) - y = 100 tan (60)

y (tan (60) - 1) = 100 tan (60)

y = 100 tan (60) / (tan (60) - 1)

y = 236.6 m

Find x:

x = y = 236.6 m

Answer: The tower is 236.6 m