Exercise 21 Page 661

Let's analyze the given right triangle.

We will find the missing measures one at a time. In this case, this means that we want to find m ∠ G, m ∠ J, and GJ.

Angle Measures

We can find m ∠ G using a tangent ratio.

The tangent of ∠ G is the ratio of the length of the leg opposite ∠ G to the length of the leg adjacent ∠ G. Tangent=Opposite/Adjacent ⇒ tan G =21/36 By the definition of the inverse tangent, the inverse tangent of 2136 is the measure of ∠ G. To find it we have to use a calculator.

m∠ G=tan ^(-1) 21/36

UseCalc

Use a calculator

m∠ G = 30.25643...

RoundInt

Round to nearest integer

m ∠ G ≈ 30

To find m∠ J, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ J and m ∠ G add to 90. m ∠ J + m ∠ G = 90 Now, we can substitute the rounded measure of ∠ G in our equation and find the measure of ∠ J. m ∠ J + 30 = 90 ⇔ m ∠ G ≈ 60

Side Lengths

Finally, we can find the measure of GJ. To do so we can use the Pythagorean Theorem. (HJ)^2 + (GH)^2 = (GJ)^2 Let's substitute the known lengths, HJ =21 and GH= 36, into this equation to find GJ.

(HJ)^2 + (GH)^2 = (GJ)^2

SubstituteII

HJ= 21, GH= 36

21^2+ 36^2= (GJ)^2

▼

Solve for GJ

CalcPow

Calculate power

441+1296=(GJ)^2

AddTerms

Add terms

1737=(GJ)^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(1737)=GJ

UseCalc

Use a calculator

41.67733... ≈ GJ

RoundDec

Round to 1 decimal place(s)

41.7≈ GJ

RearrangeEqn

Rearrange equation

GJ ≈ 41.7