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Adjacent sides of a parallelogram differ in length by 3 cm. The perimeter is 60 cm and the area is 45 cm2. What is the measure of an acute angle of the parallelogram?
Wiki User
∙ 7y ago
Let the length of the shorter sides be x cm long; then the longer sides are x + 3 cm long
Using the perimeter x can be found:
perimeter = x + x+3 + x + x+3 = 4x + 6 = 60
→ 4x = 54
x = 13.5 cm
Longer side = x + 3 = 13.5 + 3 = 16.5
Using one of the longer sides as the base of the parallelogram the height (perpendicular distance between the base and its parallel side) of the parallelogram can be found from the area:
area = base × height
→ 45 cm² = 16.5 cm × height
→ height = 45/16.5 cm = 2 8/11 cm
Using trigonometry, the sine of the angle is the height over the shorter side which forms the hypotenuse of a right angle triangle:
sin θ = (2 8/11) / 13.5 = 20/99
→ θ = arcsin(20/99) ≈ 11.66°
You could use the shorter side as the base in which case the longer side is the hypotenuse and:
height = 45/13.5 cm = 3 1/3 cm
sin θ = (3 1/3) / 16.5 = 20/99
→ θ = arcsin(20/99) ≈ 11.66°
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoApprox 11.655 degrees.
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