a guy wire reaches from the top of a 125 meter television transmitter tower to the ground.The wire makes a 63' angle with the ground.Find the length of the guy wire.
Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent.
To remember, memorize as SOH, CAH, TOA.
Where A = Adjacent, H = Hypotenuse, O = Opposite.
Since we were given the opposite side and one angle & we're to find the hypotenuse, therefore, you use
Sin 63 = Opposite/Hypotenuse
Sin 63 = 125/Hyp.
:�6¦1 Hyp = 125/Sin 63
....
To find the length of the guy wire, we can use trigonometry.
First, let's draw a diagram to visualize the problem. The tower is vertical and the guy wire makes a 63-degree angle with the ground.
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Tower /
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Ground
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In this right triangle, the guy wire is the hypotenuse, the side opposite the 63-degree angle. We are given the height of the tower, which is 125 meters, and we need to find the length of the guy wire.
Using the trigonometric function sine, we can set up the following equation:
sin(63 degrees) = opposite/hypotenuse
sin(63 degrees) = 125 meters / hypotenuse
To solve for the hypotenuse (length of the guy wire), we can rearrange the equation:
hypotenuse = 125 meters / sin(63 degrees)
Now we can calculate the length of the guy wire using a scientific calculator or any calculator with trigonometric functions.
hypotenuse ≈ 141.5 meters
Thus, the length of the guy wire is approximately 141.5 meters.