In a right-angled triangle with a hypotenuse c, one of the legs is a. find the second leg if: c = 9 a = 6

Let’s write the Pythagorean Theorem
“The square of the hypotenuse is equal to the sum of the squares of the legs.”

a² + b² = c²,

where a and b are the legs of a right-angled triangle, c is the hypotenuse.

Hypotenuse c and leg a are given to us in the problem statement.

Let us express from the Pythagorean Theorem leg b of a right triangle
b² = c² – a²;

b = √ (c² – a²);

Let’s make calculations
b = √ (9² – 6²) = √ (81 – 36) = √45 = √ (9 × 5) = 3√5.

Let’s check:

6² + (3√5) ² = 9²;

36 + 9 × 5 = 81;

36 + 45 = 81;

81 = 81.

We decided correctly.

Answer: the second leg of a right-angled triangle is 3√5.