We are told that some land is in the shape of a triangle and we are given the distances between each vertex of this triangle. We want to find the area of the land using the Law of Cosines. Let's start by making a diagram.
Before using this formula, we need to know one of the angle measures of our triangle. This is where we will use the Law of Cosines. Since angle ∠B is the largest, we will find its measure.
b^2= a^2+ c^2-2 a ccos B
Let's substitute a= 210, b= 300, and c= 140 to isolate cos B.
Now, knowing the measure of ∠B we can use the formula for the area of a triangle using sine with the sine of ∠B.
Area=1/2 a csin B
Let's substitute a= 210, c= 140 and m∠B= 116.57^(∘).
