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 degree, 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.
Let's call the length of each light string "x".
From the given information, we can form the following right triangle:
- The height of the pole (opposite side) is 7 feet.
- The length of each light string (hypotenuse) is "x".
- The angle each light string makes with the ground (angle θ) is 73.5 degrees.
We can use the sine ratio to determine the length of each light string.
Sine(θ) = Opposite / Hypotenuse
sin(θ) = 7 / x
To find "x", we isolate it by multiplying both sides of the equation by "x":
x * sin(θ) = 7
Now, let's substitute the given angle (73.5 degrees) into the equation:
x * sin(73.5) = 7
Using a calculator, we find that sin(73.5) ≈ 0.9613.
So we have:
x * 0.9613 = 7
Finally, we can solve for "x" by dividing both sides of the equation by 0.9613:
x = 7 / 0.9613 ≈ 7.28 ft
Therefore, each light string must be approximately 7.3 feet long (rounded to the nearest tenth) to reach the top of the pole.