We will find the missing measures one at a time. In this case, this means that we want to find the measures of ∠ R and ∠ T, and the length of the segment RS.
The sine of ∠ R is the ratio of the length of the leg opposite ∠ R to the length of the hypotenuse.
Sine=Opposite/Hypotenuse ⇒ sin R =6/9
By the definition of the inverse sine, the inverse sine of 69 is the measure of ∠ R. To find it, we have to use a calculator.
To find m∠ T, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ T and m ∠ R add to 90.
m ∠ T + m ∠ R = 90
Now, we can substitute the rounded measure of ∠ R in our equation and find the measure of ∠ T.
m ∠ T + 42 = 90 ⇔ m ∠ T ≈ 48
Side Lengths
Finally, we can find the measure of RS. To do it, we can use the Pythagorean Theorem.
(RS)^2 + (ST)^2 = (RT)^2
Let's substitute the known lengths, ST =6 and RT= 9, into this equation to find RS.
