Exercise 24 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 b.

Angle Measures

The sine of ∠ A is the ratio of the length of the leg opposite ∠ A to the length of hypotenuse. sin A=Opposite/Hypotenuse ⇒ sin A =17/22 By the definition of the inverse sine, the inverse sine of 1722 is the measure of ∠ A. To find it, we have to use a calculator.

m∠ A=sin ^(-1) 17/22

UseCalc

Use a calculator

m∠ A = 50.59943... ^(∘)

RoundDec

Round to 1 decimal place(s)

m∠ A ≈ 50.6 ^(∘)

To find m∠ B, recall that the acute angles of a right triangle are complementary. Therefore, m ∠ A and m ∠ B add up to 90^(∘). m ∠ A + m ∠ B = 90^(∘) Now, we can substitute the measure of ∠ A in our equation and find the measure of ∠ B. 50.6 ^(∘)+ m ∠ B ≈ 90^(∘) ⇔ m ∠ B ≈39.4^(∘)

Side Lengths

Finally, we can find the measure of b. To do it, we can use the Pythagorean Theorem. a^2 + b^2 = c^2 Let's substitute the known lengths, a= 17 and c= 22, into this equation to find b.

a^2+b^2=c^2

SubstituteII

a= 17, c= 22

17^2+b^2= 22^2

▼

Solve for c

CalcPow

Calculate power

289+b^2=484

SubEqn

LHS-289=RHS-289

b^2=195

SqrtEqn

sqrt(LHS)=sqrt(RHS)

b=sqrt(195)

UseCalc

Use a calculator

b=13.964240...

RoundDec

Round to 1 decimal place(s)

b≈ 14.0