Find the angles that form the diagonal of a rectangle with its sides, if it contains: 1) diagonal = 6

| July 5, 2021 | education

Find the angles that form the diagonal of a rectangle with its sides, if it contains: 1) diagonal = 6, side = 3√3x 2) sides are 9√3x and 9

Let us denote the rectangle given by the condition ABCD.
1. Consider a right-angled triangle ABC, in which the hypotenuse AC = 6 cm and one of the legs BC = 3√3 cm are known. By the Pythagorean theorem, we find the second leg AB:
AB = √ (AC² – BC²) = √ (36 – 27) = √9 = 3 (cm).
The AB leg is equal to half of the hypotenuse, we conclude that the angle ACB = 30 °, then the angle BAC = 90 ° – 30 ° = 60 °.
Answer: the diagonal makes angles of 30 ° and 60 ° with the sides.
2. Consider a right-angled triangle ABC. Now two legs are known, we find the hypotenuse (diagonal) of the AC:
AC = √ (AB² + BC²) = √ (81 + 243) = √324 = 18 (cm).
We got a situation similar to the first task. The hypotenuse is twice the leg. The angles are 30 ° and 60 °.
Answer: the diagonal makes angles of 30 ° and 60 ° with the sides.



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