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
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.
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