SOLUTION: In the design of a new building., a doorway is 2.65 ft above the ground. A ramp for the disabled, at an angle of 6.0 degrees with the ground, is to be built to the doorway. How lon

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Question 624353: In the design of a new building., a doorway is 2.65 ft above the ground. A ramp for the disabled, at an angle of 6.0 degrees with the ground, is to be built to the doorway. How long will the ramp be?
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Answer by jsmallt9(3758) (Show Source):
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Draw a right triangle with horizontal and vertical sides. Label the vertical side as 2.65 ft. Label the angle between the horizontal side and the hypotenuse as 6 degrees. We are looking for the length of the ramp, which is the hypotenuse, so label it "x".

To find the length of the ramp we will need to use a Trig function the involves the angle and side we know and the side we want to know. The vertical side is the side opposite to the 6 degree angle and the ramp is the hypotenuse. Which functions have ratios involving opposite and hypotenuse? Answer: sin and csc. Since 6 degrees is not a special angle we will need to use our calculator. And since our calculator probably has a button for sin but not one for csc, we will use sin. Since sin is opposite over hypotenuse the equation we have is:

Now we solve this for x. We can get rid of the fraction by multiplying both sides by x:

And then we divide by sin(6):

This is an exact expression for the answer. For a decimal approximation we reach for our calculators. First we find sin(6):

So the ramp will be approximately 25.35 feet long.