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 length of the foot of the sail given the other two side lengths and the measure of the included angle. Let f represent the length of the foot.
Using the Law of Cosines, we can write an equation for f.
f^2= 55^2+ 62^2-2( 55)( 62)cos 47^(∘)
Let's solve the equation. Notice that, since f represents a length, we will consider only a positive case when taking a square root of f^2.
