SOLUTION: A straight 120ft culvert is built down a hillside that makes an angle of 54.0 degrees with the horizontal. Find the height of the hill? help would be greatly appreciated. Thank

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Question 624333: A straight 120ft culvert is built down a hillside that makes an angle of 54.0 degrees with the horizontal. Find the height of the hill?
help would be greatly appreciated. Thank you
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
It might help to draw a triangle. Since horizontal is mentioned and height is a vertical distance, draw a right triangle with horizontal and vertical sides. The acute angle on the horizontal is 54 degrees. The culvert is the hypotenuse so label the hypotenuse as 120 ft. The side we want to find is the vertical side so label that side "x".

To solve this problem we need to pick a trig function that will involve the angle and side we have and the side we want. Since the "x" is opposite to the angle we know and the 120 is the hypotenuse, we need a function that has opposite and hypotenuse in it. So can choose sin or csc. Since 54 is not a special angle we will need our calculator. And since most calculators have a sin button but not a csc button, we'll choose sin.

Since sin is opposite/hypotenuse, the equation we will use is:

Now we solve it. Multiplying both sides by 120 we get:

This is an exact expression of the answer. For a decimal approximation we reach for our calculators:

So the height of the hill is approximately 97 ft.