the 40ft. pole is braced by , a wire from its top in a point 60ft. from its base up, snd 18° slope. how long is the wire?
To find the length of the wire, we can use trigonometry. In this case, we have a right triangle formed by the pole, the wire, and the ground. The height of the triangle is 40 ft, and the distance from the base of the pole to the point where the wire is attached is 60 ft.
To find the length of the wire, we can use the sine function. The sine of an angle is equal to the ratio of the opposite side to the hypotenuse. In this case, the opposite side is the height of the triangle (40 ft) and the hypotenuse is the length of the wire.
sin(angle) = opposite/hypotenuse
The angle given is 18°, so we can rewrite the equation as:
sin(18°) = 40 ft / hypotenuse
Rearranging the equation to solve for the hypotenuse:
hypotenuse = 40 ft / sin(18°)
Using a calculator, we find that sin(18°) is approximately 0.3090. Plugging this value into the equation:
hypotenuse = 40 ft / 0.3090
hypotenuse ≈ 129.52 ft
Therefore, the length of the wire is approximately 129.52 ft.