Question

A party tent is used for an outdoor event. Ropes of equal length support each tent pole. The angle the rope makes with the floor is 55 degrees.

What is the height of each pole? Round your FINAL answer to the nearest tenth.

Answer 1

Law of sines can be used to solve this problem:

(note - let x represent the missing side length.)

1. set up proportion.
sin 90°/25 = sin 55°/x

2. solve.
(x) sin 90° = (25) sin 55°

(x) sin 90 °/sin 90° = (25) sin 55° / sin 90°

x = 20.4788011072
rounded to nearest tenth = 20.5

Answer 2

The solution for right triangles is to use the basic trigonometric function:
For this problem, the length of the hypotenuse is given and we are looking for the side opposite, thus we will use sin x.
where
x= 55 degrees
h=25 m
sin x= side opposite/hypotenuse
sin55=sideopposite/25m
25msin55=side opposite
side opposite = 20.5 m