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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