1. Friday, February 5
Essential Questions
How do I use inverse sine, cosine, and tangent functions to find the angles of a triangle?

2. 5.4 Solve Right Triangles Let be an acute angle.
Inverse Trigonometric Ratios
Let be an acute angle.

3. 5.4 Solve Right Triangles Because tan A = _____ = _____ = _____,
Example 1
Use an inverse tangent to find an angle measure
Use a calculator to approximate the measure of to the nearest tenth of a degree.
Because tan A = _____ = _____ = _____,
Using a calculator,
So, the measure of is approximately _______.

4. 5.4
Solve Right Triangles
Checkpoint. Complete the following exercises.
In Example 1, use a calculator and an inverse tangent to approximate to the nearest tenth of a degree.

5. 5.4 Solve Right Triangles Solution Example 2 sin A = 0.76 cos B = 0.17
Use an inverse sine and an inverse cosine
Let and be acute angles in two right triangles. Use a calculator to approximate the measure of and to the nearest tenth of a degree.
sin A = 0.76
Solution
cos B = 0.17

6. 5.4 Solve Right Triangles Find by using the Triangle Sum Theorem.
Example 3
Solve a right triangle
Solve the right triangle. Round your answer to the nearest tenth.
Solution
Step 1
Find by using the Triangle Sum Theorem.

7. 5.4 Solve Right Triangles Approximate BC using a ______ ratio. sine
Example 3
Solve a right triangle
Solve the right triangle. Round your answer to the nearest tenth.
Solution
Step 2
Approximate BC using a ______ ratio.
sine
Write ratio for _________.
Multiply each side by ___.
Approximate ________.
Simplify and round answer.

8. 5.4 Solve Right Triangles Approximate AC using a ______ ratio. cosine
Example 3
Solve a right triangle
Solve the right triangle. Round your answer to the nearest tenth.
Solution
Step 3
Approximate AC using a ______ ratio.
cosine
Write ratio for _________.
Multiply each side by ___.
Approximate ________.
Simplify and round answer.

9. 5.4
Solve Right Triangles
Example 3
Solve a right triangle
Solve the right triangle. Round your answer to the nearest tenth.
Solution
The angle measures are _____, _____, and _____.
The side lengths are _____ feet, about _______ feet, and about ______ feet.

10. 5.4
Solve Right Triangles
Checkpoint. Complete the following exercises.
Find to the nearest tenth of a degree if cos T = 0.64.
Find to the nearest tenth of a degree if sin D = 0.48.

11. 5.4
Solve Right Triangles
Checkpoint. Complete the following exercises.
Solve a right triangle that has a 50o angle and a 15 inch hypotenuse.

12. 5.4
Solve Right Triangles
Pg. 187, 5.4 #1-30