The sine of ∠A is the ratio of the length of the leg opposite ∠A to the length of the hypotenuse.
Sine=Opposite/Hypotenuse ⇒ sin A =8/17
By the definition of the inverse sine, the inverse sine of 817 is the measure of ∠A. To find it, we will use a calculator.
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 rounded measure of ∠A in our equation and find the measure of ∠B.
28.1^(∘) + m∠B = 90^(∘) ⇔ m ∠B =61.9^(∘)
Side Length
Finally, we can find the measure of b. To do it, we can use the Pythagorean Theorem.
a^2 + b^2 = c^2
Let's substitute the known lengths, a = 8 and c= 17, into this equation to find b.
