# In a right-angled triangle, one leg is 6 cm, the hypotenuse is 9 cm.

October 9, 2021 | education

| **In a right-angled triangle, one leg is 6 cm, the hypotenuse is 9 cm. Find the second leg and the height drawn from the top of the right angle.**

The sum of the squares of the legs is equal to the square of the hypotenuse, we can find the unknown leg: 9 ^ 2-6 ^ 2 = 81-36 = 45. The second leg is √45 = 3√5. The area of this triangle can be found as half the product of the legs, as well as half the product of the hypotenuse and the height drawn from a right angle. S = 0.5 * 6 * 3√5 = 9√5. The height can be found by dividing twice the area by the hypotenuse: h = 2 * 9√5 / 9 = 2√5.

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