# How do you find the measure of angle B for the triangle with the following dimensions. A = 45° , a = 60.5 , b = 90?

Nov 11, 2015

You would use the Law of Sines

#### Explanation:

To set up the Law of Sines equation for this problem, which looks like this:

$\frac{a}{S} \in A$=$\frac{b}{S} \in B$=$\frac{c}{S} \in C$

You have enough information to get started. So plugging in the information given you get:

$\frac{60.5}{S} \in 45$ = $\frac{90}{S} \in B$

Upon rearrangement

$\frac{90 S \in 45}{60.5}$ = $S \in 1.051894$

Then taking the inverse sine of this number:

$S {\in}^{-} 1 \left(1.051894\right)$= domain error

With practice you'll be able to look at this and see that this particular triangle isn't possible because you have a number bigger than 1. When you take the inverse sine of this number you will get a domain error.