The tangent of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the leg adjacent ∠ A. We know that a is equal to the length of the leg opposite ∠ A and that 5.7 is equal to the length of the leg adjacent ∠ A. Therefore, we can write the following equation.
Tangent=Opposite/Adjacent ⇒ tan 34.2 ^(∘) =a/5.7
To solve this equation, we will first isolate a. Then, we will have to use the calculator to find the value of tan 34.2 ^(∘).
Now, we can find c using the Pythagorean Theorem.
a^2 + b^2 = c^2
Let's substitute the known lengths, a = 3.9 and b= 5.7, into this equation to find c.
To find m∠ B, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ A and m ∠ B add up to 90^(∘).
m ∠ A + m ∠ B = 90^(∘)
Now, we can substitute the measure of ∠ A in our equation and find the measure of ∠ B.
34.2^(∘) + m ∠ B = 90^(∘) ⇔ m ∠ B =55.8^(∘)
