Trey wants to use string lights to build a flagpole lighted tree in his front yard. Trey already has a 7-foot-tall pole mounted in the ground. If the angle each light string makes with the ground is 73.5°, use the sine ratio to determine how long each light string must be to reach the top of the pole. Round the answer to the nearest tenth. (1 point)

Question

Trey wants to use string lights to build a flagpole lighted tree in his front yard. Trey already has a 7-foot-tall pole mounted in the ground. If the angle each light string makes with the ground is 73.5°, use the sine ratio to determine how long each light string must be to reach the top of the pole. Round the answer to the nearest tenth. (1 point)

Answer 1

Let's call the length of each light string "x".

We know that the height of the flagpole is 7 feet.

Using the sine ratio, we can set up the equation:
sin(73.5°) = 7/x

To solve for x, we can rearrange the equation:
x = 7/sin(73.5°)

Using a calculator, we find that sin(73.5°) is approximately 0.9626.

So x ≈ 7/0.9626 ≈ 7.27

Therefore, each light string must be approximately 7.27 feet long.