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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 23 Page 704

Notice that the given figure is a 45^(∘)-45^(∘)-90^(∘) triangle.

x=4sqrt(2), y=45^(∘)

Practice makes perfect

Consider the given triangle.

Notice that the legs of the given right triangle are congruent. Therefore, we have an isosceles triangle and the acute angles are also congruent. By the Triangle Angle Sum Theorem, they must both measure 45^(∘).

Therefore, we have that y= 45^(∘). In a 45^(∘)-45^(∘)-90^(∘) triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of a leg.

8=sqrt(2) * x

▼

Solve for x

.LHS /sqrt(2).=.RHS /sqrt(2).

8/sqrt(2)=x

a/b=a * sqrt(2)/b * sqrt(2)

8sqrt(2)/sqrt(2)* sqrt(2)=x

sqrt(a)* sqrt(a)= a

8sqrt(2)/2=x

Calculate quotient

4sqrt(2)=x

Rearrange equation

x=4sqrt(2)

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