In a right triangle with a hypotenuse c, one of the legs is a. Find the second leg if: 1) c = 5, a = 3; 2) c = 3, a = 4.

In a right-angled triangle, the sum of the squares of the legs is equal to the square of the hypotenuse a ^ 2 + b ^ 2 = c ^ 2.

1) Let us express the leg b from the formula:

b = √ (c ^ 2 – a ^ 2) = √ (5 ^ 2 – 3 ^ 2) = √ (25 – 9) = √16 = 4.

2) b = √ (3 ^ 2 – 4 ^ 2) = √ (9 – 16) = √ (-7).

You cannot root out a negative number, therefore such a triangle does not exist.

Answer: 1) the second leg is 4, 2) a triangle with such parameters does not exist.