Question

You acquired a 34.5 foot rope and are excited to string it between the ground and up a tree to create a delivery system. You need the rope to make a 25° angle with the ground. How high up the tree do you need to place the rope? Include a sketch that shows all known information and clearly shows what you need to find . Show all work and give the answer rounded to the nearest tenth of a foot.

Answer 1

The height of the tree is 14.5 ft.

Explanation:

Let the height of the tree be 't'

The angle between the ground and the rope = 25°

Length of the rope = 34.5 ft.

To find :

The height of the tree.

We can use the sine to calculate the height of the tree.

sin 25° = t/34.5

sin 25° = 0.42

sin 25° = t/34.5

0.42 = t/34.5

t = 0.42 x 34.5

t = 14.5 ft.

The height of the tree is 14.5 ft.