Question

A right-angled triangle, with two sides adjacent to the right angle labeled 7 and 11 respectively, and the hypotenuse is labeled x.

Find the exact value of $x$ .

Answer 1

To find the length of the hypotenuse, we can use the Pythagorean theorem and set up an equation with the given side lengths. Simplifying the equation and taking the square root, we find that the exact value of the hypotenuse is the square root of 170.

Step-by-step explanation:

To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that for a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have 7 and 11 as the lengths of the two sides adjacent to the right angle. So, we can set up the equation as:

x^2 = 7^2 + 11^2

Simplifying, we get:

x^2 = 49 + 121

x^2 = 170

Taking the square root of both sides, we get:

x = √170

Therefore, the exact value of x is √170.