In triangle ABC, <A is a right angle, and m<B = 45  °. What is the length of BC? If your answer is not an integer, leave it in simplest radical form. A. 14√(2) ft B. 28 ft…

Question

In triangle ABC,  <A is a right angle, and m<B = 45°.

What is the length of BC? If your answer is not an integer, leave it in simplest radical form.

A. 14
`√(2)` ft
B. 28 ft
C. 14
`√(3)` ft
D. 14 ft

Answer 1

I believe it would be A

Answer 2

1. The lenght BC is the hypotenuse of the triangle and to find its value, we must apply:

Sin(α)=opposite leg/hypotenuse

The opposite leg is14 ft.
The hypotenuse is BC.
The Angle "α" is 45°.

2. Let's substitute in the formula:

Sin(α)=opposite leg/hypotenuse
Sin(45°)=14/BC

3. When we clear BC, we obtain:

BCxSin(45°)=14
BC=14/Sin(45°)

4. Then, the result is:

BC= 14√2 ft

5. What is the length of BC?

The answer is: The length of BC is 14√2 ft