A rope that is 72 m long is used to suspend a circus performer 12 m from the top of the ceiling. The rope is attached to the ground 40 m away from a point directly below the performer. Approximately how high in the air is the performer? The angle is 60

The performer is approximately 40 metres in the air

Step-by-step explanation: Please refer to the picture attached for more information.

The picture shows the entire length of the rope spanning the side AC and extends to side AB. However the rope stops at point P as shown in the diagram, which is the point where the performer is suspended. Also the rope is pinned down to a point A, which is 40 metres away from  a point B directly below the performer. The angle which the rope makes with ground is 60 degrees.

To calculate how high in the air the performer is suspended, we shall calculate the entire length of CB. The unknown part of the line, marked as x shall be the answer minus 12 m.

Using angle 60 as the reference angle, the opposite is line CB, and the hypotenuse is line CA.

Sin 60 = opposite/hypotenuse

Sin 60 = CB/60

0.8660 * 60 = CB

51.96 = CB

CB ≈ 52

The entire length of CB includes the length of the performer from the ceiling and then his height from the ground which is x. Therefore x can be calculated as follows;

12 + x = 52

x = 52 - 12

x = 40

The results show that the performer is approximately 40 metres above the ground.

im pretty sure its

(8,15)

step-by-step explanation: