1. EXAMPLE 3
Solve a right triangle
Solve the right triangle. Round decimal answers to the nearest tenth.
SOLUTION
STEP 1
Find m B by using the Triangle Sum Theorem.
180o
= 90o + 42o + m B
48o
= m B

2. Approximate BC by using a tangent ratio.
EXAMPLE 3
Solve a right triangle
STEP 2
Approximate BC by using a tangent ratio.
tan 42o =
BC70
Write ratio for tangent of 42o.
70 tan 42o
= BC
Multiply each side by 70. BC
Approximate tan. 42o 63 BC
Simplify and round answer.

3. Approximate AB by using a cosine ratio.
EXAMPLE 3
Solve a right triangle
STEP 3
Approximate AB by using a cosine ratio.
cos 42o =
70 AB
Write ratio for cosine of 42o.
AB cos 42o =
Multiply each side by AB. AB
cos 42o =
Divide each side by cos. 42o AB
Use a calculator to find cos. 42o AB
94.2
Simplify .
ANSWER
The angle measures are 42o, 48o, and 90o. The side lengths are 70 feet, about 63 feet, and about 94 feet.

4. EXAMPLE 4
Solve a real-world problem
THEATER DESIGN
Suppose your school is building a raked stage. The stage will be 30 feet long from front to back, with a total rise of 2 feet. A rake (angle of elevation) of 5o or less is generally preferred for the safety and comfort of the actors. Is the raked stage you are building within the range suggested?

5. EXAMPLE 4
Solve a real-world problem
SOLUTION
Use the sine and inverse sine ratios to find the degree measure x of the rake.
sin xo =
opp. hyp
2 30
0.0667 x
sin –
ANSWER
The rake is about 3.8o, so it is within the suggested range of 5o or less.

6. GUIDED PRACTICE
for Examples 3, and 4 3.
Solve a right triangle that has a 40o angle and a 20 inch hypotenuse.
SOLUTION X
STEP 1
Find m X by using the Triangle Sum Theorem.
180o
= 90o + 40o + m X
50o
= m X Y Z

7. Approximate YZ by using a sine ratio.
GUIDED PRACTICE
for Examples 3, and 4
STEP 2
Approximate YZ by using a sine ratio.
sin 40o =
XY20
Write ratio for sine of 40o.
20 sin 40o
= XY
Multiply each side by 20. XY
Approximate sin. 40o
12.9 BC
Simplify and round answer.

8. Approximate AB by using a cosine ratio.
GUIDED PRACTICE
for Examples 3, and 4
STEP 3
Approximate AB by using a cosine ratio.
cos 40o =
YZ 20
Write ratio for cosine of 40o.
20 cos 40o
= YZ
Multiply each side by 20. YZ
Approximate cos. 40o
15.3 YZ
Simplify and round answer.
ANSWER
The angle measures are 40o, 50o, and 90o. The side lengths are 12.9 in., about 15.3 in., and 20 in.

9. GUIDED PRACTICE
for Examples 3, and 4 4.
WHAT IF?
In Example 4, suppose another raked stage is 20 feet long from front to back with a total rise of 2 feet. Is this raked stage safe? Explain.
sin xo =
opp. hyp
2 20
0.1 x
sin –
No; the rake is 5.7° so it is slightly larger than the
suggested range.
ANSWER