We need to solve the given triangle. Let's begin by color coding the opposite angles and sides. We will also call the unknown sides a and b. It will help us use the Law of Sines later.
Let's find the measure of ∠ C, and side lengths b and a one at a time.
Finding m ∠ C
To find m ∠ C we can use the Triangle Sum Theorem. This tells us that the measures of the angles in a triangle add up to 180.
24^(∘) + 66^(∘) + m ∠ C = 180^(∘)
⇕
m ∠ C = 90^(∘)
Finding the Side Length b
To find the side length b of the given triangle, we can use the Law of Sines.
b/sin B = c/sin C
Let's substitute c= 43, m ∠ B = 66^(∘), and m ∠ C = 90^(∘) to calculate b.
We found that the given triangle is a right triangle. Therefore, we can use the Pythagorean Theorem to find the side length a of the given triangle. In our triangle, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with b≈ 39.3 and c= 43. Let's substitute these values into the formula.
