Questions: Find the missing sides of the special right triangle. The length of side BC is . (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

$Find the missing sides of the special right triangle. The length of side BC is . (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)$

Transcript text: Find the missing sides of the special right triangle. The length of side BC is $\square$ $\square$. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solution

Solution Steps

Step 1: Identify the type of special right triangle

The given triangle is a right triangle with one angle measuring 45 degrees. Since the sum of angles in a triangle is 180 degrees, and one angle is 90 degrees, the other angle must also be 45 degrees (180 - 90 - 45 = 45). This means we have a 45-45-90 right triangle.

Step 2: Recall the properties of a 45-45-90 triangle

In a 45-45-90 triangle, the two legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. In this triangle, AB and BC are the legs, and AC is the hypotenuse.

Step 3: Find the length of BC

We are given that the length of AB is 10. Since AB and BC are congruent, the length of BC is also 10.