Exercise 45 Page 166

Practice makes perfect

a This is a right triangle which means we can use the Pythagorean Theorem to calculate the unknown side.

a^2+b^2=c^2

SubstituteValues

Substitute values

x^2+18^2=30^2

▼

Solve for x

CalcPow

Calculate power

x^2+324=900

SubEqn

LHS-324=RHS-324

x^2=576

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± 24

x > 0

x= 24

We have found that the length of x is 24 units.

b Notice that the four angles together form 360^(∘). With this, we can write an equation.

(2x^(∘)+20^(∘))+2x^(∘)+x^(∘)+(3x^(∘)+20^(∘))=360^(∘) Let's solve the equation for x.

(2x+20)+2x+x+(3x+20)=360

RemovePar

Remove parentheses

2x+20+2x+x+3x+20=360

AddTerms

Add terms

8x+40=360

SubEqn

LHS-40=RHS-40

8x=320

DivEqn

.LHS /8.=.RHS /8.

x=40

Thus, x=40^(∘).

c Notice that the two triangles have two pairs of congruent angles. Therefore, we can claim that they are similar by Angle Angle Similarity. In similar shapes, the ratio between any pair of corresponding sides is always the same. Let's identify corresponding sides in the two figures.

Having identified corresponding sides, we can write an equation relating the ratios of corresponding sides. x/12=3/5 Let's solve this equation for x.

x/12=3/5

MultEqn

LHS * 12=RHS* 12

x=3/5* 12

MoveRightFacToNum

a/c* b = a* b/c

x=36/5

CalcQuot

Calculate quotient

x=7.2

Therefore, the length of x is 7.2 units.

Hints

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