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