Question

In triangle ABC, A is a right angle and mB = 45. Find BC. If your answer is not an integer, leave it in simplest radical form. Not drawn to scale O 20 ft 10 ft 20 2 ft 10 2 ft

Answer 1

$10\sqrt{2}\text{ ft}$Explanation

as we have a right triangle, we can use a trigonometric function to find the hypotenuse

so

Step 1

a)Let

$\begin{gathered} angle=m\measuredangle B=45 \\ opposite\text{ side=10 ft} \\ hypotenuse=BC \end{gathered}$

so, we need a function that relates those values, it is

$sin\theta=\frac{opposite\text{ side}}{hypotenuse}$

b) now, replace and solve for hypotenuse

$\begin{gathered} sin\theta=\frac{opposite\text{ side}}{hypotenuse} \\ sin\text{ 45=}\frac{10}{BC} \\ isolate\text{ BC} \\ BC=\frac{10}{sin\text{ 45}} \\ BC=\frac{10}{\frac{\sqrt{2}}{2}}=\frac{20}{\sqrt{2}} \\ BC=\frac{20}{\sqrt{2}} \\ Multiply\text{ by }\frac{\sqrt{2}}{\sqrt{2}} \\ BC=\frac{20}{\sqrt{2}*}\frac{\sqrt{2}}{\sqrt{2}} \\ BC=\frac{20\sqrt{2}}{2}=10\sqrt{2} \\ BC=10\sqrt{2} \end{gathered}$

so, the answer is

$10\sqrt{2}\text{ ft}$

I hope this helps you