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Core Connections Integrated II, 2015 View details

Chapter Closure

Exercise 102 Page 252

a We have been given the angle and hypotenuse of the triangle and want to determine the opposite leg labeled x. Given this information, we have to use the sine ratio to calculate x.

sin θ =Opposite/Hypotenuse

SubstituteValues

Substitute values

sin 15^(∘)=x/20

▼

Solve for x

MultEqn

LHS * 20=RHS* 20

20sin 15^(∘) =x

RearrangeEqn

Rearrange equation

x=20sin 15^(∘)

UseCalc

Use a calculator

x=5.17638...

RoundDec

Round to 3 decimal place(s)

x≈ 5.176

The side labeled x is about 5.176 meters.

b We have been given the angle and opposite leg and want to determine the adjacent leg labeled x. Given this information, we have to use the tangent ratio to calculate x.

tan θ=Opposite/Adjacent

SubstituteValues

Substitute values

tan 15^(∘) =5/x

▼

Solve for x

MultEqn

LHS * x=RHS* x

tan 15^(∘) * x=5

DivEqn

.LHS /tan 15^(∘).=.RHS /tan 15^(∘).

x=5/tan 15^(∘)