Let's analyze the right triangle that satisfies the given conditions.
We will find the missing measures one at a time. In this case, this means that we want to find m ∠A, a, and c.
Angle Measure
To find m∠A, recall that the acute angles of a right triangle are complementary. Therefore, m ∠A and m ∠B add to 90^(∘).
m ∠A + m ∠B = 90^(∘)
Now, we can substitute the measure of ∠B in our equation and find the measure of ∠A.
m ∠A + 31^(∘) = 90 ^(∘) ⇔ m ∠A = 59^(∘)
Side Lengths
We will find the length of the leg adjacent to the 31^(∘) angle. We are given the length of the leg opposite to this angle. Therefore, we will use the tangent ratio.
tan θ = opposite/adjacent
In our triangle, we have that θ = 31^(∘) and the length of the opposite leg is 19. We want to find the length of the adjacent leg.
To find the value of c, we can use Pythagorean Theorem.
a^2 + b^2 = c^2
Let's substitute the known lengths, a = 31.6 and b = 19, into this equation to find c.
