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McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 22 Page 704

Notice that the given figure is a 30^(∘)-60^(∘)-90^(∘) triangle.

x=5sqrt(3), y=10sqrt(3)

Practice makes perfect

Notice that the given right triangle has a marked angle measuring 60^(∘). Therefore, by the Triangle Angle Sum Theorem the measure of the third angle must be 30^(∘).

In a 30^(∘)-60^(∘)-90^(∘) triangle, the longer leg is sqrt(3) times the length of the shorter leg.

15=sqrt(3) * x

▼

Solve for x

DivEqn

.LHS /sqrt(3).=.RHS /sqrt(3).

15/sqrt(3)=x

ExpandFrac

a/b=a * sqrt(3)/b * sqrt(3)

15sqrt(3)/sqrt(3)* sqrt(3)=x

MultSqrt

sqrt(a)* sqrt(a)= a

15sqrt(3)/3=x

CalcQuot

Calculate quotient

5sqrt(3)=x

RearrangeEqn

Rearrange equation

x=5sqrt(3)

We found that the measure of the shorter leg is colIV5sqrt(3). Also, in a 30^(∘)-60^(∘)-90^(∘) triangle, the hypotenuse is 2 times the length of the shorter leg. y= 2 * 5sqrt(3) ⇔ y=10sqrt(3)

Subchapter links

1 Geometric Mean p.703

2 The Pythagorean Theorem and Its Converse p.703

3 Special Right Triangles p.704

4 Trigonometry p.704

5 Angles of Elevation and Depression p.705

6 The Law of Sines and Law of Cosines p.705

7 Vectors p.706

8 Dilations p.706

Exercise 22 Page 704

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