Trey wants to use string lights to build a flagpole lighted tree in his front yard. Trey already has a 7 foot tall pole pointer 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.
To determine how long each light string must be to reach the top of the pole, we can use the sine ratio.
The sine ratio states that sine of an angle is equal to the opposite side divided by the hypotenuse of a right triangle.
In this case, the opposite side is the height of the pole, and the hypotenuse is the length of the light string.
Let's denote the length of each light string as x.
Using the sine ratio, we can write the equation:
sin(73.5°) = opposite/hypotenuse
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°) ≈ 0.9613.
Therefore, x ≈ 7 / 0.9613
x ≈ 7.28
Thus, each light string must be approximately 7.28 feet long to reach the top of the pole.