Question

Need help QUICK! Given triangle ABC, which equation could be used to find the measure of angle B?

Plz look at pic for answers

Answer 1

2 Square 5/ 5

Explanation:

I got it right on the test

Answer 2

second option

Explanation:

We are going to use the acronym:

"Soh Cah Toa".

Why? It tells us the right-triangle definitions of sine, cosine, and tangent.

sine is opposite over hypotenuse.

cosine is adjacent over hypotenuse.

tangent is opposite over adjacent.

So looking at our triangle with respect to B tells us that 3 is the opposite measurement and 6 is the adjacent. No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by
`3√(5)`.

So let's look at cos(B).

`\cos(B)=(6)/(3√(5))`

We need to rationalize the denominator by multiplying top and bottom by sqrt(5):

`\cos(B)=(6√(5))/(3(5))=(2√(5))/(5)`

So now looking at sin(B).

`\sin(B)=(3)/(3√(5))`

We have to rationalize again by multiplying top and bottom by sqrt(5):

`\sin(B)=(3√(5))/(3(5))=(√(5))/(5)`.

So looking at our triangle with respect to A tells us that 3 is the adjacent measurement and 6 is the opposite. No matter what angle we are looking for in this triangle, the hypotenuse is constantly going to by
`3√(5)`.

We don't have to use any trigonometric ratios with A.