# Lesson 7EJustifying the LawsSolidify Understanding

### 1.

The chart shows the estimated population of the top states as of July 1, 2019. The total population of the United States including Washington, DC, and U.S. territories was estimated in 2019 to be . Calculate the percent of the total population for each of these states.

Rank in the Fifty States

State

Population Estimate

Percent of Total U.S. Population

California

Texas

Florida

New York

Pennsylvania

Illinois

### 2.

Wyoming has the smallest population of any state. Its population is of the total population of the United States. Approximately, how many people live in Wyoming?

### 3.

Maryland ranks . Its population is of the total population of the United States. Approximately, how many people live in Maryland?

### 4.

The land area of Wyoming is while the land area of Maryland is . Calculate the square miles per capita for Wyoming and Maryland.

### 5.

Number 1 (population) California has a land area of and number 2 Texas has a land area of . Calculate the square miles per capita for California and Texas.

### 6.

Rank Wyoming, Maryland, California, and Texas largest to smallest according to land area per capita.

1. Wyoming

2. Maryland

3. California

4. Texas

### 7.

Michigan covers a total area of . But of Michigan is covered in water. What is the land area of Michigan?

## Set

 Law of Sines: If $ABC$ is a triangle with sides $a$, $b$, and $c$, then: $\frac{a}{\mathrm{sin}A}=\frac{b}{\mathrm{sin}B}=\frac{c}{\mathrm{sin}C}$ or it can be written as: $\frac{\mathrm{sin}A}{a}=\frac{\mathrm{sin}B}{b}=\frac{\mathrm{sin}C}{c}$ Law of Cosines: If $ABC$ is a triangle with sides $a$, $b$, and $c$, then: ${a}^{2}={b}^{2}+{c}^{2}-2bc\mathrm{cos}A$ ${b}^{2}={a}^{2}+{c}^{2}-2ac\mathrm{cos}B$ ${c}^{2}={a}^{2}+{b}^{2}-2ab\mathrm{cos}C$

Use the law of sines to solve for the indicated values.

Solve for and .

Solve for and .

Solve for and .

Solve for and .

### 12.

Solve for , , and .

Use the law of cosines to solve each triangle. (Find all missing angles and sides.)

Solve for and .

Solve for and .

Solve for and .

### 16.

Solve for , , and .

### 17.

Solve for , , and .

## Go

Find the missing angle. Do NOT use a calculator. Consider drawing and triangles to reference while completing this work.