Question

ABC is a right triangle with right angle C. The length of the hypotenuse

is 9 units, and the length of the side AC is 5 units. Find the length of
BC.

Answer 1

To find the length of side BC in a right triangle ABC, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the length of the hypotenuse (AB) is given as 9 units, and the length of side AC is given as 5 units. Let's label the length of side BC as x.

According to the Pythagorean theorem, we have:

AB^2 = AC^2 + BC^2

Substituting the given values, we get:

9^2 = 5^2 + x^2

81 = 25 + x^2

Now, let's solve for x:

x^2 = 81 - 25

x^2 = 56

Taking the square root of both sides:

x = sqrt(56)

Simplifying the square root:

x = sqrt(4 * 14)

x = 2 * sqrt(14)

Therefore, the length of side BC is 2 * sqrt(14) units.