Lesson 8 Triangle Area by Trigonometry Practice Understanding

Ready

1.

The chart shows the total area of a few states in the United States. It also shows the total land area that is less because part of the total area is underwater. Use the information to calculate the percent of the state that is underwater.

State	Total Area $({mi}^{2})$	Land Area $({mi}^{2})$
Florida	$65,758$	$53,625$
Illinois	$57,914$	$55,519$
New Mexico	$121,590$	$121,298$
North Carolina	$53,819$	$48,618$
Wisconsin	$65,496$	$54,158$

Use the data in the chart to solve the problems.

2.

A dry climate is very beneficial for people with arthritis and osteoporosis. If you have these ailments, which state in the list would be best for your health?

3.

If you want to live near water, which state would be the best choice?

4.

Can you think of a different reason for your answer in #3 besides the $%$ of area underwater? Explain.

Set

5.

Find the area of $△ A B C$ in terms of sine $A$ . Explain each step.

Find the area of the triangle having the indicated sides and angle.

6.

$C = 84.5 °$ , $a = 32$ , $b = 40$

7.

$A = 29 °$ , $b = 49$ , $c = 50$

8.

$B = 72.5 °$ , $a = 105$ , $c = 64$

9.

$C = 31 °$ , $a = 15$ , $b = 14$

10.

$A = 42 °$ , $b = 25$ , $c = 12$

Go

Indicate whether you would use the Law of Sines or the Law of Cosines to solve the triangles. Then solve for the missing values.

11.

Find $m ∠ A$ , $m ∠ B$ , and $m ∠ C$ .

12.

Find $m ∠ B$ , $A C$ , and $A B$ .

13.

Find $m ∠ A$ and $m ∠ B$ and $A B$ .

14.

Find $m ∠ B$ , $A C$ , and $B C$ .