Let's begin with recalling the Law of Cosines. If â–³ 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 angle measure between Trail 1 and Trail 2. We will call it A.
Using the Law of Cosines, we can write an equation for A.
4^2= 2^2+ 3^2-2( 2)( 3)cos A
Let's solve the equation. We will start with isolating cos A.
Next let's use the inverse cosine to find the value of A.
cos A=-1/4 ⇓
A=cos^(-1)-1/4≈104.5^(∘)
The angle between Trail 1 and Trail 2 is approximately 104.5^(∘).
