Question
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?
Answers
Reiny
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
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