We will find the missing measures one at a time. In this case, this means that we want to find m ∠W, WX, and XZ.
Angle Measures
To find m∠W, recall that the acute angles of a right triangle are complementary. Therefore, m ∠W and m ∠Z add to 90.
m ∠W + m ∠Z = 90
Now, we can substitute the given measure of ∠Z in our equation and find the measure of ∠W.
m ∠W + 57 = 90 ⇔ m ∠W=33
The sine of ∠Z is the ratio of the length of the leg opposite ∠Z to the length of the hypotenuse.
sin Z=opposite/hypotenuse ⇒ sin 57^(∘) =WX/18
To find the length of WX, we have to use a calculator.
Finally, we can find the measure of XZ. To do it, we can use the Pythagorean Theorem.
(WX)^2 + (XZ)^2 = (WZ)^2
Let's substitute the known lengths, WX = 15.1 and WZ= 18, into this equation to find XZ.
