A radio transmission tower is 120 feet tall. How long should a guy wire be if it is to be attached 15 feet from the top and is to make an angle of 26 degrees with the ground? Give your answer to the nearest tenth of a foot
sin(26) = (120+15)/guywire
where guy wire is the length of the guy wire
To determine the length of the guy wire, we can use trigonometry. The guy wire will form a right triangle with the ground, with the tower acting as the vertical leg, the guy wire as the hypotenuse, and the distance from the attachment point to the top of the tower as the horizontal leg.
We can first find the length of the vertical leg of the triangle by subtracting the distance from the top of the tower. Therefore, the vertical leg is 120 - 15 = 105 feet.
Next, we can determine the length of the guy wire using the trigonometric function sine (sin). The sine of an angle is equal to the ratio of the length of the opposite side (in this case, the vertical leg) to the length of the hypotenuse (the guy wire).
Therefore, we can write the equation sin(26 degrees) = 105 feet / guy wire length.
Rearranging the equation to solve for the guy wire length, we get guy wire length = 105 feet / sin(26 degrees).
Using a calculator, we find that sin(26 degrees) is approximately 0.438. So, guy wire length = 105 feet / 0.438 = 239.726 feet.
Rounding to the nearest tenth of a foot, the length of the guy wire should be approximately 239.7 feet.
To solve this problem, we can use trigonometry, specifically the sine function. The side opposite the angle of 26 degrees is the height of the tower (120 feet), and the side adjacent to the angle is the distance from the attachment point to the top of the tower (15 feet).
Let's name the length of the guy wire as "x" feet. We can start by setting up the equation using the sine function:
sin(angle) = opposite / hypotenuse
sin(26 degrees) = 120 feet / x feet
Now, we can solve it algebraically for x. Rearranging the equation, we have:
x = 120 feet / sin(26 degrees)
Using a calculator, we can find the value for sin(26 degrees), which is approximately 0.438. Plugging in this value, we get:
x = 120 feet / 0.438
x ≈ 273.97 feet
Rounding to the nearest tenth of a foot, the length of the guy wire should be approximately 274.0 feet.