Transcript Lesson 7

5-Minute Check on Chapter 2
Transparency 3-1
1. Evaluate 42 - |x - 7| if x = -3
2. Find 4.1  (-0.5)
Simplify each expression
4. (36d – 18) / (-9)
3. 8(-2c + 5) + 9c
5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops.
If one is chosen at random, what is the probability that it is
not green?
6.
Standardized Test Practice:
Which of the following is a true
statement
A
8/4 < 4/8
B
-4/8 < -8/4
C
-4/8 > -8/4
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D
-4/8 > 4/8
Lesson 11-7
Trigonometric Ratios
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Objectives
• Define the sine, cosine, and tangent ratios
• Use trigonometric ratios to solve right
triangles
Vocabulary
•
•
•
•
•
•
Trigonometric ratios –
sine –
cosine –
tangent –
angle of elevation –
angle of depression –
Four Step Problem Solving Plan
• Step 1: Explore the Problem
– Identify what information is given (the facts)
– Identify what you are asked to find (the question)
• Step 2: Plan the Solution
– Find an equation the represents the problem
– Let a variable represent what you are looking for
• Step 3: Solve the Problem
– Plug into your equation and solve for the variable
• Step 4: Examine the Solution
– Does your answer make sense?
– Does it fit the facts in the problem?
Example 1
Find the sine, cosine, and tangent of each acute angle
of
Round to the nearest ten-thousandth.
Write each ratio and substitute the measures. Use a
calculator to find each value.
Example 1 cont
Answers:
Answer:
Example 1 cont
Answers:
Answer:
Example 2
Find cos 65° to the nearest ten thousandth.
Keystrokes COS 65
ENTER .4226182617
Answer: Rounded to the nearest ten thousandth,
Example 3
Find the measure of
to the nearest degree.
Since the lengths of the adjacent leg and
the hypotenuse are known, use the
cosine ratio.
and
Now use [COS–1] on a calculator to find the measure of
the angle whose cosine ratio is 12 / 20
Keystrokes 2nd [COS–1] 12
20
ENTER
53.13010235
Answer: To the nearest degree, the measure of
is 53°.
Example 4
Find all of the missing measures in
You need to find the measures of
and
Step 1 Find the measure of
The
sum of the measures of the
angles in a triangle is 180.
The measure of
is 28°.
Example 4 cont
Step 2 Find the value of y, which is the measure of the
hypotenuse. Since you know the measure of the
side opposite
use the sine ratio.
Definition of sine
Evaluate sin 62°.
Find the cross products.
is about 17.0 centimeters long.
Example 4 cont
Step 3 Find the value of x, which is the measure of the side
adjacent
Use the tangent ratio.
Definition of sine
Evaluate tan 62°.
Find the cross products.
is about 8.0 centimeters long.
Answer: So, the missing measures are 28, 8 cm, and 17 cm.
Example 5
Indirect Measurement In the diagram, Barone is flying
his model airplane 400 feet above him. An angle of
depression is formed by a horizontal line of sight and
a line of sight below it. Find the angles of depression
at points A and B to the nearest degree.
Explore In the diagram two right
triangles are formed. You
know the height of the
airplane and the horizontal
distance it has traveled.
Plan
Let A represent the first
angle of depression. Let
B represent the second
angle of depression.
Example 5 cont
Solve
Write two equations involving the tangent ratio.
and
Answer: The angle of depression at point A is 45° and
the angle of depression at point B is 37°.
Summary & Homework
• Summary:
– xxxxx
• Homework:
– none