We can use the sine ratio to determine the length of each light string. In this case, the opposite side is the height of the pole (7 feet) and the hypotenuse is the length of each light string. The angle is given as 73.5 degrees.
Let's use the sine ratio:
sine angle = opposite / hypotenuse
sin(73.5°) = 7 / hypotenuse
To find the hypotenuse, we can rearrange the equation:
hypotenuse = 7 / sin(73.5°)
Using a calculator, sin(73.5°) is approximately 0.9659.
hypotenuse = 7 / 0.9659
≈ 7.23
Therefore, each light string must be approximately 7.23 feet long to reach the top of the pole. Rounded to the nearest tenth, the answer is 7.2 feet.
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.
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