The heights drawn from the top of the obtuse angle of the parallelogram make up an angle of 45.

| February 9, 2021 | education

The heights drawn from the top of the obtuse angle of the parallelogram make up an angle of 45. One of the heights divides the side to which it is lowered into 2 cm and 8 cm segments, counting from the top of the acute angle. Find the area of the parallelogram. 2. The sides of the triangle are 12 cm and 9 cm, and the angle between them is 30. Find the area of the triangle.

1) AВСD – parallelogram, BH1 and BH2 heights on its sides, <H1BH2 = 45 °, then <ADС = 180 ° – 45 ° = 135 °. Now you can find the angle <ВAD = 180 ° – 135 ° = 45 °.

Triangle ABN1 is isosceles, since the angles at the base of AB are equal to 45 °. Hence, the height BH1 = AH1 = 2 (cm). Determine the area of AВСD: AD * ВН1 = (2 cm + 8 cm) * 2 cm = 10 cm * 2 cm = 20 cm².

2) The area of any triangle is simply determined by the two sides and the angle between the sides. The area is equal to:

12 cm * 9 cm * sin [<(12.9)] = 12 cm * 9 cm * sin 30 ° = 12 * 9/2 = 6 * 9 = 54 cm².



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