Final answer:
The problem is to find the length of a guy wire attached at a 30° angle using trigonometry. You can solve it by using the sine function with the pole's height and the known angle. The length of the guy wire is found to be 20 feet when the calculations are performed.
Step-by-step explanation:
The student is asking how to find the length of a guy wire that is attached to a pole at a 30° angle with the vertical. This is a trigonometry problem that can be solved using the concept of right triangles and trigonometric ratios such as sine, cosine, or tangent.
To solve for the guy wire length, we can use the sine function. In a right triangle, where the guy wire is the hypotenuse and the pole is one of the legs, we can use the trigonometric ratio sine because we have the opposite side (the height of the pole, which is 10 feet) and we want to find the hypotenuse (the guy wire length).
The sine of the angle can be expressed as the ratio of the opposite side to the hypotenuse. Therefore, sin(30°) = opposite/hypotenuse which is sin(30°) = 10 feet / guy wire length. We can then solve for the length of the guy wire.
As sin(30°) is a standard value (1/2), the equation can be simplified to 1/2 = 10 feet / guy wire length. Multiplying both sides by the guy wire length and then by 2 gives us the length of the guy wire as 20 feet.