The height of the trapezoid is 4 cm, and the corners for the larger base are 30 degrees and 45 degrees. Find the sides.
| April 28, 2021 | education
In a right-angled triangle ABН, one of its acute angles is 45, then this triangle is isosceles, AH = BH = 4 cm.
Then AB ^ 2 = AH ^ 2 + BH ^ 2 = 2 * AH ^ 2 = 2 * 16 = 32.
AB = 4 * √2 cm.
In a right-angled triangle СDК, the angle СDК, by condition, is equal to 30, then the leg СН lies opposite the angle 30, and then its length is equal to half the length of СD.
CK = CD / 2.
CD = 2 * SK = 2 * 4 = 8 cm.
Answer: The sides of the trapezoid are 8 cm and 4 * √2 cm.
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