The sine of ∠ T is the ratio of the length of the leg opposite ∠ T to the length of the hypotenuse.
sin T=opposite/hypotenuse ⇒ sin T =19/36
By the definition of the inverse sine, the inverse sine of 1936 is the measure of ∠ T. To find it, we have to use a calculator.
To find m∠ R, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ R and m ∠ T add to 90.
m ∠ R + m ∠ T = 90
Now, we can substitute the rounded measure of ∠ T in our equation and find the measure of ∠ R.
m ∠ R + 32 = 90 ⇔ m ∠ R ≈ 58
Side Lengths
Finally, we can find the measure of ST. To do it, we can use the Pythagorean Theorem.
(RS)^2 + (ST)^2 = (RT)^2
Let's substitute the known lengths, RS = 19 and RT= 36, into this equation to find ST.
