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

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.

In a right-angled triangle, the hypotenuse is equal to the leg divided by the cosine of the included angle, then the hypotenuse is:
33: 11/61 = 3 * 61 = 183.
The 2nd leg is easy to find by the Pythagorean theorem:
√ (183 ^ 2 – 33 ^ 2 = √ (33489 – 1089) = 180.
Then the perimeter of the triangle is:
183 + 33 + 180 = 396.