Question

In Triangle ABC, angle A is a right angle, and angle B = 45°. Find BC. If your answer is not aninteger, write it in radical form.

Answer 1

In a 90-45-45 triangle the legs of the triangle are equal:

$AC=BA=11ft$

And the hypotenuse is given by:

$\begin{gathered} BC=AC\sqrt[]{2} \\ so\colon \\ BC=11\sqrt[]{2} \end{gathered}$

Using sine function:

$\begin{gathered} \sin (\theta)=\frac{opposite}{hypotenuse} \\ so\colon \\ \sin (45)=\frac{AC}{BC} \\ \sin (45)=\frac{11}{BC} \\ solve_{\text{ }}for_{\text{ }}BC\colon \\ BC=\frac{11}{\sin (45)} \\ BC=11\sqrt[]{2} \end{gathered}$