Question

Two sides of a parallelogram or 320 feet and 160 feet the measure of the angle between the size is 131° find the area of a parallelogram to the nearest square foot

Answer 1

A = 38,720 sq ft

Explanation:

the formula requires you to multiply base and height; we know the base is 320 but do not know height (which is the perpendicular segment connecting both sides of 320 feet)

we can create a right triangle by drawing the height which will have a hypotenuse of 160 and we know the angle across from the height is 49° (180 minus twice 131, divided in half)

therefore, we can use the law of sines to find height:

sin 90°/1 = sin 49°/h

h = 160·sin 49° is approximately 121

A = 320 x 121 ≈ 38,720