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: 6 square root 2

Explanation:

Answer 2

`BC=6√(2)\ units`

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)=(BC)/(AB)` ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

we have

`cos(45^o)=(√(2))/(2)`

`AB=12\ units`

substitute

`BC=cos(B)(AB)`

`BC=(√(2))/(2)(12)=6√(2)\ units`