Download The Pythagorean Theorem

THE TANGENT RATIO
UNIT 10: SECTION 8.5
OBJECTI VE: TO DEFI NE THE TANGENT RATI O FOR AN ACUTE TRI ANGLE.
TO SOLVE RI GHT TRI ANGLE PROBLEMS USI NG THE TANGENT RATI O.
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.
Example 1: Use a calculator to find the value of each to the nearest
ten-thousandth.
1) sin 21°
2) tan 22°
Practice 1: Use a calculator to find the value of each to the nearest
ten-thousandth.
1) cos 20°
2) sin 77°
3) tan 17°
4) cos 87°
Find the inverse tangent, sine, and cosine keys on the calculator.
cos 1
tan 1
sin 1
Example 2: Find each angle measure to the nearest degree.
1) sin B = 0.4848
2) cos W = 0.6157
3) tan W = 19.0811
Practice 2: Find each angle measure to the nearest degree.
1) sin A = 0.5150
2) cos A = 0.7431
3) cos A = 0.5878
4) cos A = 0.4226
5) tan W = 0.5317
6) sin A = 0.7431
1) tan 24° = _________
2) tan 41° = _________
3) tan 88° = _________
4) tan ______ = 2.4751
5) tan ______ = 0.3057
6) tan ______ = 0.8098
Extra Practice:
NOW INTRODUCING
THE TANGENT RATIO
Tangent ∠x = Side Opposite ∠x
Side Adjacent ∠x
Tangent ∠x = Side Opposite ∠x
Side Adjacent ∠x
Side Adjacent ∠x
x
Side Opposite ∠x
Practice
70°
29.24
10
90°
20°
27.47
Using the given triangle, find the following measures to the nearest
hundredth.
1) leg opposite 20°
leg adjacent 20°
2) tangent 20°
3) leg opposite 70°
leg adjacent 70°
4) tangent 70°
USING THE TANGENT RATIO
Use the tan proportion to solve the following.
Example 3
x
37°
12
13.5
80°
x
Guided Practice: Find tan A, tan B, m∠A, and m∠B
1.
C
7
A
2
A
B
2.
17
B
3. Find the value of x to the
nearest tenth.
15
8
20
24°
x
C
Guided Practice: Find the value of x to the nearest tenth
10
4.
35°
x
Find y° correct to the nearest degree.
8
5.
5
y°
6.
8
6
y°
10
Closure:
1. What the name of the branch of mathematics that uses tangents, cosines,
and sines?
2. State the tangent ratio.
Homework: P308 Written Exercises: #1-18a