The hypotenuse of a right triangle is 3 times longer than one of its legs. Write the length of the third leg as a function of the known leg. (Simplify your answer)

Answer 1

x represents the length of the leg

3x represents the length of the hypotenuse

(3x)² - x² represents the other leg

Can you simplify and answer?

Answer 2

The adjacent leg would be L to the hypotenuse 3L so cos Θ = L ⁄ 3L = 1⁄3 ; so Φ = 70.5°;

sin Φ = third leg⁄ 3L so 3Lsin 70.5° = third leg = 2.83 L

To write like a function apply the Pythagorean Theorem setting the third leg as y, hypotenuse as 3x and other

leg as x. (3x²) = x² + y² ; y² = 9x² - x² = 8x²; y = 2√2 x