In a rectangular trapezoid, the acute angle is 45 degrees, the smaller side is 8 cm

univerkov | September 11, 2021 | education

In a rectangular trapezoid, the acute angle is 45 degrees, the smaller side is 8 cm, and the middle line is 28 cm. Find the upper base.

1. From the top of C we draw the perpendicular CH to the base of AD.

2. Angle DСН = 180 ° – 45 ° – 90 ° = 45 °.

3. Since the angles at the side СD are equal, the triangle DСН is isosceles. CH = DH = 8 cm.

4. CH = AB = 8 cm. DH is also equal to 8 cm.

5. AD = AH + DH. AH = BC. AD = BC + 8 cm.

5. Using the formula for the middle line of a trapezoid, we calculate the total length of the upper and lower base:

(BC + AD): 2 = 28 cm.

BC + AD = 56 cm.

BC + BC + 8 = 56 cm.

2 BC = 48 cm.

BC = 24 cm.

Answer: the length of the upper base of the BC is 24 cm.

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