1. How do I use the sine, cosine, and tangent ratios to solve triangles?
Wednesday, February 3
Essential Questions
How do I use the sine, cosine, and tangent ratios to solve triangles?

2. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Trigonometric Ratios A B C a c
CAH
TOA
SOH
SOHCAHTOA b

3. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Tangent Ratio
Let rABC be a right triangle with acute The tangent of (written as tan A) is defined as follows:

4. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Example 1
Find tangent ratios
Find tan X and tan Y. Write each answer as a fraction and as a decimal rounded to four places.
In the right triangle, rXYZ, and are _______________ angles. You can see that the tangent ratios of the _________________ angles are ___________.
complementary
complementary
reciprocals

5. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Example 2
Find a leg length
Find the value of x.
Use the tangent of an acute angle to find a leg length.
Write a ratio for tangent of 25o.
Substitute.
Multiply each side by ____.
Use a calculator to find tan 25o.
Simplify.

6. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Checkpoint. Complete the following exercises.
Find tan A and tan B. Round your answer to four decimal places.

7. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Checkpoint. Complete the following exercises.
Find the value of x. Round to the nearest tenth.

8. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Example 3
Compare the tangent ratios for similar triangles
Find tan X and tan Y for similar triangles. Then compare the tangent ratios.
The values of tan X and tan Y for the similar triangles are ________.
equivalent

9. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Example 4
Estimate height using tangent
Find the height h of the flagpole to the nearest foot.
Write ratio for tangent of 70o.
Substitute.
Multiply each side by ___.
Use a calculator to simplify.
The flagpole is about _____ feet tall. 19

10. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Checkpoint. Complete the following exercises.
Find the height h of the flagpole in Example 4 to the nearest foot if the angle is 75o.

11. Apply the Tangent Ratio
5.2
Apply the Tangent Ratio
Pg. 173, 5.2 #1-25

12. Apply the Sine and Cosine Ratios
5.3
Apply the Sine and Cosine Ratios
Pg. 218, 6.4 #1-32