Calculate the smaller side and area of the rectangle, if its larger side is 12 inches, the diagonal is 8√3 inches

| December 13, 2020 | education

Calculate the smaller side and area of the rectangle, if its larger side is 12 inches, the diagonal is 8√3 inches and forms an angle of 60 degrees with the smaller side.

Consider a triangle formed by a diagonal and two adjacent sides of a rectangle. Such a triangle is rectangular because the corners of the rectangle are straight. Since the diagonal makes an angle of 60 ° with the smaller side, the opposite side is an angle of (90-60 = 30 °) 30 °. Then, by the property of a leg opposite to an angle of 30 °: the smaller side of the rectangle is equal to half the diagonal = 1/2 * 8 * √3 = 4 * √3.
The area of a rectangle is equal to the product of its length and width = 12 * 4 * √3 = 48 √3 (dm ^ 2).
Answer: the smaller side = 4√3, the area is 48√3.



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