Expert: Sherman D. - 3/24/2005

Question
1) a building has a ramp to its front doors to accommodate the handicapped. if the distance from the building to the end of the ramp is 23 feet and the height from the ground to the front doors is 5 feet, how long is the ramp? (round to the nearest tenth).

2) 2 boats leave a dock together, each travelling in a straight line. one boat travels at 16 mph and the other at 14 mph. if the angle between their courses measures 51.9 degrees, how far apart are they after 18 minutes? give your answer in miles and round your answer to the nearest tenth.

Answer
1.)
a = 5
b = 23

a^2 + b^2 = c^2
5^2 + 23^2 = c^2
25 + 529 = c^2
554 = c^2
c = 23.5 feet

The length of the ramp is 23.5 feet.

This is using the pythagorean thereom

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2.)
after 18 minutes,
16mph = 4.8 miles
14mph = 4.2 miles

cos(A) = (c^2 + b^2 - a^2)/(2bc)
cos(51.9) = ((4.8)^2 + (4.2)^2 - a^2)/(2(4.8)(4.2))
cos(51.9) = (23.04 + 17.64 - a^2)/(2(20.16))
cos(51.9) = (40.68 - a^2)/(40.32)
40.32cos(51.9) = 40.68 - a^2
40.32cos(51.9) - 40.68 = -a^2
-40.32cos(51.9) + 40.68 = a^2
a = sqrt(-40.32cos(51.9) + 40.68)
a = sqrt(-24.87888649 + 40.68)
a = sqrt(15.80111351)
a = 3.975061448 miles
or
a = 4.0 miles

I used Laws of Cosines, at http://mathworld.wolfram.com/LawofSines.html

i used that formula, because all i had to work with was 2 sides and one angle.