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 high up the pole will it be attached?(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 high up the pole will it be attached?(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 sine function in trigonometry. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse.
In this case, the telephone pole and the ground form a right angle, the cable is the hypotenuse, and the height up the pole where the cable is attached is the opposite side. We are given the length of the hypotenuse (225 feet) and the angle of elevation (40 degrees).
We can set up the equation as follows:
sin(40) = height / 225
To solve for the height, we multiply both sides by 225:
height = 225 * sin(40)
Now we just need to calculate the value. Remember to convert the angle to radians if your calculator is set to that mode.
After calculating, round your answer to one decimal place.
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