Question

Kim uses two ropes to help support a newly planted tree. The ropes are placed on both sides of the tree and pinned to the ground, as shown in the diagram above. The length of each rope from the tree to the ground is 14 feet. The distance from the base of the tree to where it is pinned to the ground is 8 feet.

Enter the acute angle each rope makes with the ground, rounded to the nearest degree.

Answer 1

Angle = 35°

Explanation:

The figure would form a triangle and the tree will divide it into two 90 degree triangles.

Height of the triangles will be 8 feet which is opposite to the angle you have to find.

Hypotenuse of both 90 degree triangles will be 14 feet.

To find the angle, use the sin formula

sin (angle) = opposite/hypotenuse

angle = ?

opposite = 8

hypotenuse = 14

sin (angle) = 8/14

angle = sin inverse (0.57)

angle = 34.8° rounded off to 35°

The angle will be the same for both triangles.

Therefore, the acute angle each triangle makes with the ground is 35°.