A telephone transmission tower is stabilized by having cables attached at a height of 57.5 feet off the ground and then anchored in cement.The angle of elevation is 50.50. How long a cable is needed?(Answer to ONE decimal place and put only the number with no units in the answer box.)
Question
A telephone transmission tower is stabilized by having cables attached at a height of 57.5 feet off the ground and then anchored in cement.The angle of elevation is 50.50. How long a cable is needed?(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 tangent of the angle of elevation, which is the opposite side (height of the tower) divided by the adjacent side (distance from the tower to the point where the cable is anchored in the ground). However, we want to find the length of the cable, which is the hypotenuse of the right triangle formed by the tower, the ground, and the cable. So, we should use the sine of the angle of elevation, which is the opposite side (height of the tower) divided by the hypotenuse (length of the cable).
The formula is:
sin(angle) = opposite/hypotenuse
We can rearrange this to solve for the hypotenuse:
hypotenuse = opposite/sin(angle)
Substituting the given values:
hypotenuse = 57.5/sin(50.5)
Now, just calculate the right side of the equation to find the length of the cable. Make sure your calculator is set to degrees before calculating.
After calculating, round your answer to one decimal place.
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