Question

In triangle ABC, ∠A is a right angle and m∠B = 45°. Find BC. If your answer is not an integer, leave it in the simplest radical form. The question is multiple choice and the choices are below. A. 20$\sqrt{2}$ ft B. 10 ft C. 20 ft D. 10 $\sqrt{2}$ ft

Answer 1

Answer: D $10\sqrt{2}$

Step-by-step explanation:

It says that the measure of angle B is 45 degrees. So if we were to put in 45 degrees  we could see that is is opposite AC and BC which we needs to find is the hypotenuse. So since we know the opposite of angle B  is 10 ft we can using that to find the length of BC.  Opposite hypotenuse is the sine function so we will use it to calculate the length of BC.

sin(45) = $\frac{10}{BC}$       multiply both sides by BC  

BC sin(45) = 10      divide both sides by sin(45)

BC = $\frac{10}{sin(45)}$

BC = $10\sqrt{2}$

Answer 2

Answer:

$\huge\boxed{Option\ D : \ BC = 10\sqrt{2}\ ft }$

Step-by-step explanation:

Since it's a right angled triangle, We'll use trigonometric rations.

Given that m∠B = 45°

So,

Sin B = opposite / hypotenuse

Where m∠B = 45°, opposite = 10 ft and hypotenuse = BC

Sin 45 = 10 / BC

$\sf \frac{\sqrt{2} }{2} = \frac{10}{BC}$

BC = 20 / √2

Multiplying and Dividing by √2

BC = 20√2 / √(2)²

BC = 20 √2 / 2

BC = 10√2 ft