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 ∠B, b, and c.
Angle Measure
To find m∠B, 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 ∠A in our equation and find the measure of ∠B.
36^(∘) +m ∠B = 90^(∘) ⇔ m ∠B = 54^(∘)
Side Lengths
Next, we will find the length of the leg adjacent to the 36^(∘) 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 = 36^(∘) and the length of the opposite leg is 12. We want to find the length of the adjacent leg.
To find the value of c, we can use the Pythagorean Theorem.
a^2 + b^2 = c^2
Let's substitute the known lengths, a = 12 and b = 16.5, into this equation to find c.
