# The leg of a right-angled triangle is 9 cm, and the cosine of the included angle is 0.6. Find the perimeter of the triangle.

October 10, 2021 | education

| First, we find the sine of the angle adjacent to the leg through the basic trigonometric identity (sin ^ 2 (a) + cos ^ 2 (a) = 1): sin ^ 2 (a) + 0.36 = 1; sin ^ 2 (a) = 1 – 0.36 = 0.64; sin (a) = 0.8.

Next, we find the tangent of this angle (tg (a) = sin (a) / cos (a)): tg (a) = 0.8 / 0.6 = 4/3.

In a right-angled triangle, the leg is equal to the product of the other leg by the tangent of the adjacent angle (b = a * tg (a)): b = 9 * (4/3) = 12.

Let’s find the length of the hypotenuse through the Pythagorean theorem: c ^ 2 = 12 ^ 2 + 9 ^ 2 = 144 + 81 = 225; c = 15.

P = a + b + c = 9 + 12 + 25 = 46.

Answer: 46.

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