1. THE Tangent Ratio Unit 10: Section 8.5
Objective: To Define the tangent ratio for an acute Triangle.
To Solve Right Triangle problems using the tangent ratio.

2. Find the tangent, sine, and cosine keys on the calculator.
Trigonometry
Trignometry – comes from the Greek words that mean “triangle measurement. Our Study will be limited to the trigonometry of Right Triangle.
Purpose (video link) : Introduce the very important ratio, called the tangent ratio, that is formed by using the lengths of the legs of a right triangle.
BUT FIRST – EVERYONE NEEDS A CALCULATOR
Find the tangent, sine, and cosine keys on the calculator.

3. Find the inverse tangent, sine, and cosine keys on the calculator.
Example 1: Use a calculator to find the value of each to the nearest
ten-thousandth.
1) sin 21° ) tan 22°
Practice 1: Use a calculator to find the value of each to the nearest
ten-thousandth.
cos 20° ) sin 77°
3) tan 17° ) cos 87°
Find the inverse tangent, sine, and cosine keys on the calculator.

4. Example 2: Find each angle measure to the nearest degree.
1) sin B = ) cos W = ) tan W =
Practice 2: Find each angle measure to the nearest degree.
sin A = ) cos A = ) cos A =
4) cos A = ) tan W = ) sin A =
Extra Practice:
tan 24° = _________ 2) tan 41° = _________ 3) tan 88° = _________
4) tan ______ = ) tan ______ = ) tan ______ =

5. THE TANGENT RATIO NOW INTRODUCING Side Adjacent ∠x
Tangent ∠x = Side Opposite ∠x
Side Adjacent ∠x

6. Side Adjacent ∠x Tangent ∠x = Side Opposite ∠x Side Adjacent ∠x x

7. Practice
70°
29.24 10
90°
20°
27.47
Using the given triangle, find the following measures to the nearest hundredth.
leg opposite 20° 2) tangent 20°
leg adjacent 20°
3) leg opposite 70° 4) tangent 70°
leg adjacent 70°

8. USING THE TANGENT RATIO
Use the tan proportion to solve the following.
Example 3 x
37° 12
13.5
80° x

9. Guided Practice: Find tan A, tan B, m∠A, and m∠B1. 2.
Find the value of x to the
nearest tenth. 7 C A 2 A B 17 15 B C 8 20
24° x

10. Guided Practice: Find the value of x to the nearest tenth4.
Find y° correct to the nearest degree. 5. 6. 10
35° x 8 5 y° 8 6 y° 10

11. Closure:
What the name of the branch of mathematics that uses tangents, cosines, and sines?
State the tangent ratio.
Homework: P308 Written Exercises: #1-18a