Question

unit exam - right triangles and trigonometry
find the indicated side of the right triangle.
11
x
45°
11
$x = \square\sqrt{\square}$

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so legs are equal.

Step2: Apply Pythagorean theorem

For right triangle, $c^2 = a^2 + b^2$, where $c=x$, $a=11$, $b=11$.
$$x^2 = 11^2 + 11^2$$

Step3: Calculate sum of squares

$$x^2 = 121 + 121 = 242$$

Step4: Solve for x

$$x = \sqrt{242} = \sqrt{121 \times 2} = 11\sqrt{2}$$

Answer:

$x = 11\sqrt{2}$