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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[tex] \sqrt{2} [/tex] ft
B. 28 ft
C. 14 [tex]\sqrt{3} [/tex] ft
D. 14 ft

In triangle ABC ltA is a right angle and mltB 45 What is the length of BC If your answer is not an integer leave it in simplest radical form A 14tex sqrt2 tex f class=

Respuesta :

I believe it would be A

carlosego
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

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