Question

In the right triangle shown, m\angle A=45\degreem∠A=45°m, angle, A, equals, 45, degree and AB = 12AB=12A, B, equals, 12. How long is BC

Answer 1

Answer:

$BC=6\sqrt{2}\ units$

Step-by-step explanation:

In this problem i will assume that the side AB is the hypotenuse

The picture in the attached figure

we know that

In a right triangle, if one angle is 45 degrees, then the other angle complementary is equal to 45 degrees too

so

$m\angle B=45^o$

In the right triangle ABC

$cos(B)=\frac{BC}{AB}$ ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

we have

$cos(45^o)=\frac{\sqrt{2}}{2}$

$AB=12\ units$

substitute

$BC=cos(B)(AB)$

$BC=\frac{\sqrt{2}}{2}(12)=6\sqrt{2}\ units$