The hypotenuse of a right-angled triangle is 82 cm, and the tangent of one of the corners is 9/40

The hypotenuse of a right-angled triangle is 82 cm, and the tangent of one of the corners is 9/40. Find the legs of this triangle.

From the condition it is known that the legs of the triangle are related to each other as 9 to 40.

We enter the coefficient of similarity x and then we can write the lengths of the legs as 9x one and then the second 40x.

We apply the Pythagorean theorem to a right-angled triangle and get the equation. Let’s remember the Pythagorean theorem:

c ^ 2 = a ^ 2 + b ^ 2.

The square of the hypotenuse is equal to the sum of the squares of the legs:

(9x) ^ 2 + (40x) ^ 2 = 82 ^ 2;

81x ^ 2 + 1600x ^ 2 = 6724.

We solve the resulting incomplete quadratic equation:

1681x ^ 2 = 6724;

x ^ 2 = 4;

x = 2.

Then one leg is 9x = 18 cm, the second leg is 40x = 80 cm.