1. Geometry
Section 7.7

3. EXAMPLE 1
Use an inverse tangent to find an angle measure
Use a calculator to approximate the measure of A to the nearest tenth of a degree.
SOLUTION
Because tan A =
1520 34 =
= 0.75,
tan–1 0.75
= m A
Use a calculator tan –
ANSWER
So, the measure of A is approximately 36.9o.

4. EXAMPLE 2
Use an inverse sine and an inverse cosine
Let A and B be acute angles in a right triangle. Use a calculator to approximate the measures of A and B to the nearest tenth of a degree. a.
sin A = 0.87 b.
cos B = 0.15
SOLUTION a.
m A
= sin –1 0.87
60.5o b.
m B
= cos –
81.4o

5. Solve the right triangle. Round decimal answers to the nearest tenth.
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
Multiple Solutions
48o
= m B

6. 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.

7. 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.

8. Solve the right triangleB A C