A telephone pole is being stabilized by attaching a 227 foot cable to the pole and anchoring it to the ground a distance away from the base.If the angle of elevation is 33.60, 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 227 foot cable to the pole and anchoring it to the ground a distance away from the base.If the angle of elevation is 33.60, 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 in this case is the distance from the base of the pole to the anchor point) divided by the hypotenuse (which is the length of the cable).
So, we can set up the equation as follows:
cos(33.60) = adjacent / 227
To find the adjacent side (the distance from the base of the pole to the anchor point), we rearrange the equation to solve for the adjacent side:
adjacent = 227 * cos(33.60)
Now, we just need to plug in the values and calculate:
adjacent = 227 * cos(33.60) = 187.9
So, the cable should be anchored approximately 187.9 feet from the base of the pole.
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