Question 209396
Admiral Al needs a ramp to perform a stunt at the Arlington High School pep rally. For the first 20 feet along the ground, the ramp must rise off of the ground at a constant rate. After the construction crew had finished 5 feet of the horizontal distance, the track is 4 feet off the ground. After 20 feet of horizontal distance is constructed, Admiral Al needs to clear a 12 foot high barrier. Will he be able to do it?
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Draw the picture of two overlapping right triangles.
The smaller triangle has a base of 5 and height of 4.
The larger has a base of 20 and a height of 12 ft.
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Find the angle of elevation of the smaller triangle.
tan^-1(4/5) = 38.66 degrees
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Using that angle solve for the height of the triangle when the base is 20.
tan(38.66) = height/20
height = 20*tan(38.66) = 20*0.8 = 16
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Al's going to make it as his height is 16 and the barrier is only 12 ft.
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Cheers,
Stan H.
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