Exercise 9 Page 214

To determine the triangle's perimeter, we need to find all of its sides. To find the opposite side of the 17^(∘) angle we can use the tangent ratio. tan( θ)=opposite/adjacent Let's identify the opposite and adjacent leg to the 17^(∘) angle in our diagram.

Let's solve this equation.

tan 17^(∘)=9/b

MultEqn

LHS * b=RHS* b

btan 17^(∘)=9

DivEqn

.LHS /(tan 17^(∘)).=.RHS /(tan 17^(∘)).

b=9/tan 17^(∘)

UseCalc

Use a calculator

b=29.43767...

RoundDec

Round to 2 decimal place(s)

b ≈ 29.44

When we know the length of the second leg, we can determine the hypotenuse by using the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteII

a= 9, b= 29.44

9^2+ 29.44^2=c^2

▼

Solve for c

CalcPow

Calculate power

81+866.7136=c^2

AddTerms

Add terms

947.71356=c^2

RearrangeEqn

Rearrange equation

c^2=947.71356

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c=± sqrt(947.71356)

c > 0

c=sqrt(947.71356)

When we know all three sides, we can find the perimeter by adding them. 9+29.44+sqrt(947.71356)≈ 69.22cm