The sine of ∠ B is the ratio of the length of the leg opposite ∠ B to the length of the hypotenuse. We know that b is equal to the length of the leg opposite ∠ B and that 20 is equal to the length of the hypotenuse. Therefore, we can write the following equation.
sin B=Opposite/Hypotenuse ⇒ sin 8.3 ^(∘) =b/20
To solve this equation, we will first isolate b. Then, we will have to use the calculator to find the value of sin 8.3 ^(∘).
To find m∠ A, 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 ∠ B in our equation and find the measure of ∠ A.
m ∠ A+8.3^(∘) = 90^(∘) ⇔ m ∠ A =81.7^(∘)
