A telephone pole is being stabilized by attaching a 225 foot cable to the pole and anchoring it to the ground a distance away from the base.If the angle of elevation is 400, how far from the base should the cable be anchored into the ground?(Answer to ONE decimal place and put only the number with no units in the answer box.)
Question
A telephone pole is being stabilized by attaching a 225 foot cable to the pole and anchoring it to the ground a distance away from the base.If the angle of elevation is 400, how far from the base should the cable be anchored into the ground?(Answer to ONE decimal place and put only the number with no units in the answer box.)
Solution
To solve this problem, we can use the trigonometric function cosine. The cosine of an angle in a right triangle is equal to the adjacent side (which is the distance from the base of the pole to the anchor point we're trying to find) divided by the hypotenuse (which is the length of the cable).
The formula is:
cos(angle) = adjacent/hypotenuse
We know the angle is 40 degrees and the hypotenuse is 225 feet. We want to find the adjacent side (the distance from the base of the pole to the anchor point), so we rearrange the formula to solve for the adjacent side:
adjacent = cos(angle) * hypotenuse
First, we need to convert the angle from degrees to radians because the cosine function in most calculators uses radians. There are π radians in 180 degrees, so to convert degrees to radians, we multiply by π/180:
40 degrees * π/180 = 0.6981 radians
Then we substitute the angle and the hypotenuse into the formula:
adjacent = cos(0.6981) * 225
Finally, we calculate the result:
adjacent = 0.7660 * 225 = 172.4
So, the cable should be anchored 172.4 feet away from the base of the pole. Since the question asks for the answer to one decimal place, we round to 172.4.
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