Question

In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit. The zip line extends from the top of a tower to a point on the ground 60 feet away from the base of the tower. The angle of elevation of the zip line is 20°. Estimate the length of the zip line to the nearest tenth of a foot.

about 63.9 ft

about 21.8 ft

about 175.4 ft

about 164.8 ft

Answer 1

Using relations in a right triangle, it is found that the length of the zip line is of about 63.9 ft.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

• The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

• The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

• The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, the hypotenuse is the length of the line, considering that the base of 60 ft is adjacent to the angle of 20º, hence:

$\cos{20^\circ} = \frac{60}{l}$

$l = \frac{60}{\cos{20^\circ}}$

$l = 63.9$

The length of the zip line is of about 63.9 ft.

More can be learned about the relations in a right triangle at https://brainly.com/question/18090623