The sine of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the hypotenuse. We know that a is equal to the length of the leg opposite ∠ A, and therefore we can write the following equation.
Sine=Opposite/Hypotenuse ⇒ sin 52 ^(∘) =a/10
To solve this equation, we will first isolate a. Then, we will have to use the calculator to find the value of sin 52 ^(∘).
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.
52^(∘) + m ∠ B = 90^(∘) ⇔ m ∠ B =38.0^(∘)
