Exercise 19 Page 379

To determine the triangles perimeter, we need to find all of its sides. To find the opposite side of the 60^(∘) angle we can use the tangent ratio. tan θ=opposite/adjacent Let's identify the opposite and adjacent leg to the 60^(∘) angle in our diagram.

Let's solve this equation.

tan60=x/6

MultEqn

LHS * 6=RHS* 6

6tan 60=x

RearrangeEqn

Rearrange equation

x=6tan 60

UseCalc

Use a calculator

x =10.39230...

RoundDec

Round to 2 decimal place(s)

x ≈ 10.39

When we know the length of the second leg, we can determine the hypotenuse, y, by using the Pythagorean Theorem. Notice that the exact length of the vertical leg is 6tan(60^(∘)). To avoid any rounding errors, we will use this value as the length.

a^2+b^2=c^2

SubstituteII

a= 6, b= 6tan(60^(∘))

( 6)^2+( 6tan 60)^2=y^2

▼

Solve for y

CalcPow

Calculate power

36+108=y^2

AddTerms

Add terms

144=y^2

RearrangeEqn

Rearrange equation

y^2=144

SqrtEqn

sqrt(LHS)=sqrt(RHS)

y=± 12

y > 0

y=12