SOLUTION: the base angles of a trapezoid are 29° and 75° respectively, if the top and bottom bases of the trapezoid measure 86m and 147m respectively, find the product of the diagonals

Question 1153284: the base angles of a trapezoid are 29° and 75° respectively, if the top and bottom bases of the trapezoid measure 86m and 147m respectively, find the product of the diagonals
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Draw this
angle A is 29 degrees and angle B is 75 degrees
C is the top left and D the top right.
Make a rectangle with top and bottom 86 m., drawing lines from C to E on the AB line and D to F on the AB line
Triangle DFB is a right triangle and tangent 75=h/x, where h is the height.
Triangle CAE is a right triangle and tangent 29=h/(61-x)
We know EF is 86, we call FB x, so AE must be 61-x to make the line 147m
from the first, we get h=3.732x
from the second, we get h=tan 29(61-x) and that is 33.813-0.5543 x
set those two equal to each other , and one will get h=29.45
FB=7.89 and AE is 53.11. All units are m
Now diagonal AD is the hypotenuse of right triangle AFD with legs 139.11 and 29.45. With the Pythagorean theorem, AD is 142.19 m
Similarly, triangle BEC is a right triangle with legs 29.45 and 93.89. Using the Pythagorean theorem, BC is 98.40 m
The product of 142.19 and 98.40=13,991.50 m^2

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