Question

If the two shorter sides of a right triangle are 90 and 75, find the length of the longest side of the triangle to the nearest hundredth.

Answer 1

The length of the longest side, or hypotenuse, of the right triangle with shorter sides of 90 and 75 can be found using the Pythagorean theorem. The length is approximately 117.07 units.

Step-by-step explanation:

The longest side of a right triangle, also known as the hypotenuse, can be found using the Pythagorean theorem. The theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have two shorter sides of lengths 90 and 75.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse as follows:

c^2 = a^2 + b^2

c^2 = 90^2 + 75^2

c^2 = 8100 + 5625

c^2 = 13725

c = √13725 ≈ 117.07

Therefore, the length of the longest side of the triangle is approximately 117.07 units.