Exercise 5 Page 316

Practice makes perfect

a We have been given the adjacent leg to the reference angle and are asked to find the length of the angle's opposite leg. With this information, we have to use the tangent ratio.

tan θ =Opposite/Adjacent

Let's identify these sides in our diagram and substitute them into the equation.

Let's solve for x in our equation.

tan 44^(∘) =x/28

MultEqn

LHS * 28=RHS* 28

28 tan 44^(∘) = x

RearrangeEqn

Rearrange equation

x= 28 tan 44^(∘)

UseCalc

Use a calculator

x= 27.03928...

RoundDec

Round to 2 decimal place(s)

x≈ 27.04

b We have been given the adjacent leg to the reference angle and are asked to find the length of the hypotenuse. With this information, we have to use the cosine ratio.

cos θ =Adjacent/Hypotenuse

Let's identify these sides in the diagram and substitute them into the cosine ratio.

Let's solve for x in this equation.

cos 32^(∘) =150/x

MultEqn

LHS * x=RHS* x

xcos 32^(∘) =150

DivEqn

.LHS /cos 32^(∘).=.RHS /cos 32^(∘).

x = 150/cos 32^(∘)

UseCalc

Use a calculator

x= 176.87676...

RoundInt

Round to nearest integer

x≈ 176.88

c We have been given the hypotenuse and are are asked to find the length of the opposite leg to the reference angle. With this information, we have to use the sine ratio.

sin θ =Opposite/Hypotenuse

Let's identify these sides in the diagram and substitute them into the sine ratio.