Let's begin with recalling the Law of Cosines. If △ ABC has lengths of a, b, and c and angle measures of A, B, and C, then we can write equations that relate the side lengths of this triangle and the cosine of one of its angles.
Now let's take a look at the given picture. We are asked to evaluate the distance between Memphis and Huntsville, which we can call d.
Using the Law of Cosines, we can write an equation for d.
d^2= 90^2+ 122^2-2( 90)( 122)cos 153.9^(∘)
Let's solve the equation. Notice that, since d represents a length, we will consider only a positive case when taking a square root of d^2.
