Exercise 38 Page 925

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 a.

Angle Measures

The sine of ∠ B is the ratio of the length of the leg opposite ∠ B to the length of the hypotenuse. sin B=Opposite/Hypotenuse ⇒ sin B =8/17 By the definition of the inverse sine, the inverse sine of 817 is the measure of ∠ B. To find it, we have to use a calculator.

m∠ B=sin ^(-1) 8/17

UseCalc

Use a calculator

m∠ B = 28.07248... ^(∘)

RoundDec

Round to 1 decimal place(s)

m∠ B ≈ 28.1 ^(∘)

To find m∠ A, 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 approximated measure of ∠ B in our equation and find the measure of ∠ A. m ∠ A + 28.1 ^(∘) ≈ 90^(∘) ⇔ m ∠ A ≈ 61.9^(∘)

Side Lengths

Finally, we can find the measure of a. To do it, we can use the Pythagorean Theorem. a^2 + b^2 = c^2 Let's substitute the known lengths, b = 8 and c= 17, into this equation to find c.

a^2+b^2=c^2

SubstituteII

b= 8, c= 17

a^2 + 8^2= 17^2

▼

Solve for a

CalcPow

Calculate power

a^2+64=289

SubEqn

LHS-64=RHS-64

a^2=225

SqrtEqn

sqrt(LHS)=sqrt(RHS)

a=sqrt(225)

UseCalc

Use a calculator

a=15.0