Exercise 21 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 a.

Angle Measures

The sine of ∠ B is the ratio of the length of the leg opposite ∠ B to the length of hypotenuse. sin B=Opposite/Hypotenuse ⇒ sin B =12/15 By the definition of the inverse sine, the inverse sine of 1215 is the measure of ∠ B. To find it, we have to use a calculator.

m∠ B=sin ^(-1) 12/15

UseCalc

Use a calculator

m∠ B = 53.13010... ^(∘)

RoundDec

Round to 1 decimal place(s)

m∠ B ≈ 53.1 ^(∘)

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 + 53.1 ^(∘) ≈ 90^(∘) ⇔ m ∠ A ≈36.9^(∘)

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 = 12 and c= 15, into this equation to find a.

a^2+b^2=c^2

SubstituteII

b= 12, c= 15

a^2 + 12^2= 15^2

▼

Solve for a

CalcPow

Calculate power

a^2+144=225

SubEqn

LHS-114=RHS-114

a^2=81

SqrtEqn

sqrt(LHS)=sqrt(RHS)

a=sqrt(81)

UseCalc

Use a calculator

a=9.0