Exercise 22 Page 924

First, let's draw the measurements from the exercise on a right triangle to visualize the given information.

We will find the missing measures one at a time. In this case, this means that we want to find m ∠ A, m ∠ B, and c.

Angle Measures

We can find m ∠ A using a tangent ratio. The tangent of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of the leg adjacent ∠ A. tan A=Opposite/Adjacent ⇒ tan A =8.1/6.2 By the definition of the inverse tangent, the inverse tangent of 8.16.2 is the measure of ∠ A. To find it, we have to use a calculator.

m∠ A=tan ^(-1) 8.1/6.2

UseCalc

Use a calculator

m∠ A = 52.56839... ^(∘)

RoundDec

Round to 1 decimal place(s)

m∠ A ≈ 52.6 ^(∘)

To find m∠ B, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ B and m ∠ A add to 90^(∘). m ∠ A + m ∠ B = 90^(∘) Now, we can substitute the approximated measure of ∠ A in our equation and find the measure of ∠ B. 52.6 ^(∘) + m ∠ B ^(∘) ≈ 90^(∘) ⇔ m ∠ B ≈37.4^(∘)

Side Lengths

Finally, we can find the measure of c. To do it, we can use the Pythagorean Theorem. a^2 + b^2 = c^2 Let's substitute the known lengths, a = 8.1 and b= 6.2, into this equation to find c.

a^2+b^2=c^2

SubstituteII

a= 8.1, b= 6.2

8.1^2 + 6.2^2= c^2

▼

Solve for c

CalcPow

Calculate power

65.61+38.44=c^2

AddTerms

Add terms

104.05=c^2