Question

The pivot point (P) of the main supporting arm (AP) of a construction crane is 46 metres above the top of a 96 metre tall office building. When the supporting arm is at an angle of 55° to the horizontal, the length of cable dropping from the point A to the ground is 215 metres. Find the length of the main supporting arm (AP), to the nearest centimetre.

Answer 1

Answer: Let's call the length of the main supporting arm AP = x.

We can use the Pythagorean theorem to find the length of the cable dropping from point A to the ground:

c^2 = x^2 + (46 - 96 + 215)^2

c^2 = x^2 + (175 - 50)^2

c^2 = x^2 + 125^2

c^2 = x^2 + 15625

Since the angle between the main supporting arm and the horizontal is 55°, we can use the trigonometric relationship between the length of the opposite side (the cable) and the length of the adjacent side (the main supporting arm) to find x:

tan 55° = c / x

x / c = tan 55°

x / 215 = tan 55°

x = 215 * tan 55°

The value of x can be calculated using a scientific calculator or by using a table of tangent values. To the nearest centimetre, x = 204 cm.

Explanation: