Question 1042258: The two non-parallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°.
(a) Find the length of the diagonal.
(b) Find the length of the shorter base.
Show all your work and explain how you arrived at your answer. Round answers to the nearest hundredth.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It helps to draw it.
Since it is isosceles, the angles are the same and must be 70 degrees.
sin 70=x/7, and that is the height of the trapezoid, or 6.58 feet
cos 70=y/7, and that is half the distance that the longer base is over the shorter base.
y=7 cos 70=2.39 feet
The longer base is 4.79 (rounding) feet greater than the shorter base, so the shorter is 17.21 feet long.
The diagonal: The base of the right triangle for which the diagonal is the hypotenuse is 22-2.39=19.61 feet long. The height is 6.58 feet. Square both and have 384.390+43.268=427.658. The hypotenuse is the square root of that.
The square root of that is 20.68 feet. Diagonal.
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