To find the desired angle measure, we will start by drawing a diagram to illustrate the situation.
To find the value of m ∠U, it will be useful to first find the value of s. We know that the lengths of t and u are 8 and 10 inches, respectively. We also know that their included angle has a measure of 96^(∘). With this information and using the Law of Cosines, we can write an equation to find s.
Note that we only kept the principal root when solving the equation, because s is the length of a side. Let's add the value of s to our diagram.
Now, notice that we know the values of m ∠S, as well as of s and u. This means that we use the Law of Sines to find the value of m ∠U. Using this law, we can form the following equation.
sin( m ∠U)/u = sin( m ∠S)/s
Let's substitute the known values into the above equation and solve it for m∠U.
