Question

The angle of elevation of an unfinished tower from a point of 120m away from its base is 25 degrees. How much higher will the tower need to be raised so that its angle of elevation from the same point will be 40 degrees?

Answer 1

Answer:

44.73 m

Step-by-step explanation:

Given that the angle of elevation of an unfinished tower from a point of 120m away from its base is 25 degrees.

Using trigonometry ratio, the height of the tower can be calculated by

Tan Ø = height / base

Tan 25 = height / 120

Make height the subject of formula

Height = 120 × tan 25

Height = 55.96 m

How much higher will the tower need to be raised so that its angle of elevation from the same point will be 40 degrees?

Using the same formula to calculate the new height.

Tan 40 = new height / base

Tan 40 = new height / 120

Make the new height the subject of the formula.

New height = 120 × tan 40

New height = 100.69 m

Increase in height = new height - height

Increase in height = 100.69 - 55.96

Increase in height = 44.73m

Therefore, the tower will need 44.73m to be raised so that its angle of elevation from the same point will be 40 degrees.