In a triangle, a leg is given, the length of which is 33, and the cosine of the adjacent

| April 29, 2021 | education

In a triangle, a leg is given, the length of which is 33, and the cosine of the adjacent acute angle is 11/61. Find the perimeter of the triangle.

Answer: 396 cm.
Decision:
Let’s designate the known leg AC = 33 cm. The unknown leg is BA, the hypotenuse is BC. In a right-angled triangle, the cosine of the angle is equal to the ratio of the adjacent leg to the hypotenuse. We know the cos of the angle adjacent to the AC, i.e. cos (α) = 11/61 = AC / BC, AC / BC = 11/61, 33 / BC = 11/61, BC = 183 (cm).
Find the unknown leg using the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
BC² = AC² + BA², BA² = 183²-33² = 32400, VA = √ (32400) = 180 (cm).
Perimeter: P = BC + AC + BA = 183 + 33 + 180 = 396 (cm).



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