Question

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

Answer 1

`BC = 12√(2)`

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
`(1)/(√(2) )` so we can substitute this value instead to get the answer in simple radical form.

`(1)/(√(2) ) = \frac {12} {BC}`

`BC = (12)/((1)/(√(2) ))`

`BC = 12√(2)`

Answer 2

ANSWER


`|BC|=12√(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 * {12}^(2)`


`|BC| = \sqrt{ {12}^(2) * 2 }`


`|BC|=12√(2)\: ft`