Question

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

Answer 1

ANSWER

$|BC|=12\sqrt{2}\: ft$

EXPLANATION

The given right triangle is an isosceles triangle because

$m \: < \: B = 45 \degree = m \: < \: C$
This implies that,

$|AB|=12ft=|AC|$

From the Pythagoras Theorem,

$|BC|^2=|AB|^2+|AC|^2$

$|BC|^2= {12}^{2} + {12}^{2}$

$|BC|^2=2 \times {12}^{2}$

$|BC| = \sqrt{ {12}^{2} \times 2 }$

$|BC|=12\sqrt{2}\: ft$

Answer 2

Answer:

$BC = 12\sqrt{2}$

Step-by-step explanation:

We are given a right angled triangle ABC with the side AC 12 feet long while the measure of the angle B is 45 degrees.

We are to find the length of the side BC. For that, we can use the sine function:

$sin 45 = \frac {12} {BC}$

Since sin 45 is equal to $\frac{1}{\sqrt{2} }$ so we can substitute this value instead to get the answer in simple radical form.

$\frac{1}{\sqrt{2} } = \frac {12} {BC}$

$BC = \frac{12}{\frac{1}{\sqrt{2} }}$

$BC = 12\sqrt{2}$