# How do you solve a triangle given a=6.3. b=9.4, <C=38.3° ?

##### 1 Answer

#### Explanation:

Here is what I think the triangle looks like:

**By the Law of Cosines:**

using the given values for

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

**By the Law of Sines:**

with given and determined values

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The conversion of

into

is **only valid provided angle A is acute**

If a triangle has an obtuse angle, that angle will be opposite the longest side (note there can be at most one obtuse angle).

In other words, if an angle is opposite a side which is not the longest side, that angle must be acute.

It is therefore safe to use the Law of Sines to evaluate

The largest angle (the angle opposite the longest side) should **always** be evaluated as