body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Glencoe Geometry, 2012

MH

McGraw Hill Glencoe Geometry, 2012 View details

4. Trigonometry

Continue to next subchapter

Exercise 43 Page 575

Recall that the acute angles of a right triangle are complementary. You can use this fact to find the measure of ∠ W.

m ∠ W =33
WX ≈ 15.1
XZ ≈ 9.8

Practice makes perfect

Let's analyze the given right triangle.

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

Side Lengths

We can find WX using a sine ratio.

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.

sin 57^(∘)=WX/18

▼

Solve for WX

LHS * 18=RHS* 18

sin 57^(∘) * 18=WX

Rearrange equation

WX=sin 57^(∘) * 18

Use a calculator

WX=15.09607...

Round to 1 decimal place(s)

WX≈ 15.1

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.

(WX)^2 + (XZ)^2 = (WZ)^2

WX= 15.1, WZ= 18

( 15.1)^2+(XZ)^2= 18^2

▼

Solve for XZ

Calculate power

228.01+(XZ)^2=324

LHS-228.01=RHS-228.01

(XZ)^2= 95.99

sqrt(LHS)=sqrt(RHS)

XZ= sqrt(95.99)

Use a calculator

XZ = 9.79744...

Round to 1 decimal place(s)

XZ≈ 9.8

Subchapter links

Check Your Understanding p.573

Practice and Problem Solving p.573-576

H.O.T. Problems p.576

Standardized Test Practice p.577

Spiral Review p.577

Skills Review p.577