the base of a trapezoid are 22 and 12 respectively. the angle at the extremities of one base are 65 degree and 45 degree respectively. find two legs?

Answer 1

label the parallelogram ABCD, where AD = 12, BC = 22
angle B = 45° and angle C = 65°

draw a line DE || AB to meet BC at E
Thus, BE = 12, and EC = 10
label AB = DE = x
and DC = y
clearly, angle DEC = 45°

In triangle DEC,
sin45/y = sin65/x = sin70/10

sin45/y = sin70/10
ysin70 = 10sin45
y = 10sin45/sin70 = appr 7.525

sin65/x = sin70/10
xsin70 = 10sin65
x = 10sin65/sin70 = appr 9.645