Questions: Find the unknown length in the right triangle shown to the right. The unknown length in the given right triangle is in. (Type an integer or decimal rounded to the nearest thousandth as needed.)

Find the unknown length in the right triangle shown to the right.

The unknown length in the given right triangle is in.
(Type an integer or decimal rounded to the nearest thousandth as needed.)

Transcript text: Find the unknown length in the right triangle shown to the right. The unknown length in the given right triangle is $\square$ in. (Type an integer or decimal rounded to the nearest thousandth as needed.)

Solution

Solution Steps

Step 1: Apply the Pythagorean theorem

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the lengths of the two sides are 9 in and 40 in, and we want to find the length of the hypotenuse. Let the unknown length be represented by $c$. Then we can write the equation as: $c^2 = 9^2 + 40^2$

Step 2: Calculate the squares

$c^2 = 81 + 1600$

Step 3: Add the squared values

$c^2 = 1681$

Step 4: Solve for c

Taking the square root of both sides: $c = \sqrt{1681}$ $c = 41$