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Title: Splash Screen

1
Splash Screen
2
Five-Minute Check (over Chapter
11) CCSS Then/Now New Vocabulary Key Concept
Trigonometric Functions in Right
Triangles Example 1 Evaluate Trigonometric
Functions Example 2 Find Trigonometric
Ratios Key Concept Trigonometric Values for
Special Angles Example 3 Find a Missing Side
Length Example 4 Find a Missing Side Length Key
Concept Inverse Trigonometric Ratios Example 5
Find a Missing Angle Measure Example 6 Use
Angles of Elevation and Depression
3
5-Minute Check 1
When a triangle is a right triangle, one of its
angles measures 90. Does this show correlation
or causation? Explain.
A. Causation a triangle must have a 90 angle to
be a right triangle. B. Causation a triangles
angles must add to 180. C. Correlation a
triangle must have a 90 angle to be a right
triangle. D. Correlation a triangles angles
4
5-Minute Check 2
From a box containing 8 blue pencils and 6 red
pencils, 4 pencils are drawn and not replaced.
What is the probability that all four pencils are
the same color?
5
5-Minute Check 3
A. accept B. reject
6
5-Minute Check 4
Jenny makes 60 of her foul shots. If she takes
5 shots in a game, what is the probability that
she will make fewer than 4 foul shots?
7
CCSS
Mathematical Practices 6 Attend to precision.
8
Then/Now
You used the Pythagorean Theorem to find side
lengths of right triangles.
• Find values of trigonometric functions for acute
angles.
• Use trigonometric functions to find side lengths
and angle measures of right triangles.

9
Vocabulary
• trigonometry
• trigonometric ratio
• trigonometric function
• sine
• cosine
• tangent
• cosecant
• secant
• cotangent
• reciprocal functions
• inverse sine
• inverse cosine
• inverse tangent
• angle of elevation
• angle of depression

10
Concept
11
Example 1
Evaluate Trigonometric Functions
Find the values of the six trigonometric
functions for angle G.
Use opp 24, adj 32, and hyp 40 to write
each trigonometric ratio.
12
Example 1
Evaluate Trigonometric Functions
13
Example 1
Evaluate Trigonometric Functions
14
Example 1
Find the value of the six trigonometric functions
for angle A.
15
Example 2
Find Trigonometric Ratios
16
Example 2
Find Trigonometric Ratios
Step 2 Use the Pythagorean Theorem to find c.
a2 b2 c2 Pythagorean Theorem 32
52 c2 Replace a with 3 and b with
5. 34 c2 Simplify.
Take the square root of each side. Length
cannot be negative.
17
Example 2
Find Trigonometric Ratios
Step 3
Now find csc A.
Cosecant ratio
18
Example 2
19
Concept
20
Example 3
Find a Missing Side Length
Use a trigonometric function to find the value of
x. Round to the nearest tenth if necessary.
The measure of the hypotenuse is 12. The side
with the missing length is opposite the angle
measuring 60?. The trigonometric function
relating the opposite side of a right triangle
and the hypotenuse is the sine function.
21
Example 3
Find a Missing Side Length
Sine ratio
Replace ? with 60, opp with x, and hyp
with 12.
Multiply each side by 12.
10.4 x
Use a calculator.
22
Example 3
Write an equation involving sin, cos, or tan that
can be used to find the value of x. Then solve
the equation. Round to the nearest tenth.
23
Example 4
Find a Missing Side Length
BUILDINGS To calculate the height of a building,
Joel walked 200 feet from the base of the
building and used an inclinometer to measure the
angle from his eye to the top of the building. If
Joels eye level is at 6 feet, what is the
distance from the top of the building to Joels
eye?
24
Example 4
Find a Missing Side Length
Cosine function
Use a calculator.
Answer The distance from the top of the
building to Joels eye is about 827 feet.
25
Example 4
TREES To calculate the height of a tree in his
front yard, Anand walked 50 feet from the base of
the tree and used an inclinometer to measure the
angle from his eye to the top of the tree, which
was 62. If Anands eye level is at 6 feet,
about how tall is the tree?
A. 43 ft B. 81 ft C. 87 ft D. 100 ft
26
Concept
27
Example 5
Find a Missing Angle Measure
A. Find the measure of ?A. Round to the nearest
tenth if necessary.
You know the measures of the sides. You need to
find m? A.
Inverse sine
28
Example 5
Find a Missing Angle Measure
Use a calculator.
29
Example 5
Find a Missing Angle Measure
B. Find the measure of ?B. Round to the nearest
tenth if necessary.
Use the cosine function.
30
Example 5
A. Find the measure of ?A.
A. m?A 72º B. m?A 80º C. m?A 30º D. m?A
55º
31
Example 5
B. Find the measure of ?B.
A. m?B 18º B. m?B 10º C. m?B 60º D. m?B
35º
32
Example 6
Use Angles of Elevation and Depression
A. GOLF A golfer is standing at the tee, looking
up to the green on a hill. The tee is 36 yards
lower than the green and the angle of elevation
from the tee to the hole is 12. From a camera in
a blimp, the apparent distance between the golfer
and the hole is the horizontal distance. Find the
horizontal distance.
33
Example 6
Use Angles of Elevation and Depression
Write an equation using a trigonometric function
that involves the ratio of the vertical rise
(side opposite the 12 angle) and the horizontal
distance from the tee to the hole (adjacent).
Multiply each side by x.
Divide each side by tan 12.
Simplify.
x 169.4
Answer So, the horizontal distance from the tee
to the green as seen from a camera in a blimp is
34
Example 6
Use Angles of Elevation and Depression
B. ROLLER COASTER The hill of the roller coaster
has an angle of descent, or an angle of
depression, of 60. Its vertical drop is 195
feet. From a blimp, the apparent distance
traveled by the roller coaster is the horizontal
distance from the top of the hill to the bottom.
Find the horizontal distance.
35
Example 6
Use Angles of Elevation and Depression
Write an equation using a trigonometric function
that involves the ratio of the vertical drop
(side opposite the 60 angle) and the horizontal
Multiply each side by x.
Divide each side by tan 60.
Simplify.
x 112.6
Answer So, the horizontal distance of the hill
36
Example 6
A. BASEBALL Mario hits a line drive home run from
3 feet in the air to a height of 125 feet, where
it strikes a billboard in the outfield. If the
angle of elevation of the hit was 22, what is
the horizontal distance from home plate to the
billboard?
A. 295 ft B. 302 ft C. 309 ft D. 320 ft
37
Example 6
B. KITES Angelina is flying a kite in the wind
with a string with a length of 60 feet. If the
angle of elevation of the kite string is 55,
then how high is the kite in the air?
A. 34 ft B. 49 ft C. 73 ft D. 85 ft
38
End of the Lesson