Question

find u.
√6 in
45°
45°
u
write your answer in simplest radical form.
inches
√
submit

Explanation:

Step1: Identify Triangle Type

The triangle has two 45° angles and a right angle, so it's a 45-45-90 triangle. In such triangles, the legs are equal, and the hypotenuse \( h = l\sqrt{2} \), where \( l \) is a leg. Here, the hypotenuse is \( \sqrt{6} \), and we need to find leg \( u \).

Step2: Use 45-45-90 Ratio

For a 45-45-90 triangle, \( \text{leg} = \frac{\text{hypotenuse}}{\sqrt{2}} \). Substitute hypotenuse \( \sqrt{6} \):
\( u = \frac{\sqrt{6}}{\sqrt{2}} \)

Step3: Simplify the Radical

Rationalize or simplify: \( \frac{\sqrt{6}}{\sqrt{2}} = \sqrt{\frac{6}{2}} = \sqrt{3} \) (using \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \)).

Answer:

\( \sqrt{3} \)