A trapezoid ABCD with a right angle A is given. Its base is 5cm and 12cm, and one of the angles

univerkov | February 25, 2021 | education

A trapezoid ABCD with a right angle A is given. Its base is 5cm and 12cm, and one of the angles is 60 degrees. Find the sides of the CD.

1. CH – height. ∠D = 60 °.

2. CH divides the trapezoid into two geometric shapes: the ABCH rectangle and the CDH triangle.

In a rectangle, the sides opposite each other (opposite) are equal:

BC = AH = 5 centimeters.

3. DH = 12 – 5 = 7 centimeters.

4. Calculate the length of the side СD, which is the hypotenuse in the right-angled triangle СDН in terms of the cosine ∠D:

DH: CD = cosine ∠D = 60 ° = cosine 60 ° = 1/2.

СD = DH: 1/2 = 7: 1/2 = 14 centimeters.

Answer: СD = 14 centimeters.

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