Since all three side lengths are known, we can use the Law of Cosines to find any angle measure.
Explanation: See solution. Angle Measure: 102^(∘)
Practice makes perfect
We are told that a triangle has side lengths of 10.6 centimeters, 8 centimeters, and 14.5 centimeters. Let's start with drawing this triangle.
We need to explain how to find the measure of the largest angle and then find it. We will do those things one at a time.
Explanation
First, note that we can use the Law of Cosines to find any measure in our triangle, because we know all three side lengths.
This is how we can find the measure of the largest angle, but first we need to identify it. The largest angle is situated opposite to the longest side. Therefore, in our case the largest angle is ∠B. This means we will need to use the second version of the Law of Cosines.
b^2= a^2+ c^2-2 a csin B
Finding the Measure
We already know that we need to find the measure of angle ∠B using the Law of Cosines. Let's substitute a= 8, b= 14.5, and c= 10.6.
