SOLUTION: Given: ABCD - rectangle O is intersection of diagnals of the rectangle AABCD = 458m2 m∠AOB = 80° Find: AB, BC

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Question 1147669: Given: ABCD - rectangle
O is intersection of diagnals of the rectangle
AABCD = 458m2
m∠AOB = 80°
Find: AB, BC

Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


With angle AOB 80 degrees, side AB is a short side and BC is a long side of the rectangle.

AOB 80 degrees --> BOC 100 degrees --> ACB = 40 degrees

AB/BC = tan(40)
AB = BC*tan(40) [1]
Area = AB*BC = (BC)^2*tan(40) = 458 [2]

Solve [2] for BC; then use [1] to find AB.

Check your work by verifying that AB*BC = 458.