CONFIDENTIAL2 Warm Up Find the geometric mean of each pair of a
number. 1) 3 and 27 2) 6 and 24 3) 8 and 32
Slide 3
CONFIDENTIAL3 Trigonometric Ratios By the AA Similarity
Postulate, a right triangle with a given acute angle is similar to
every other right triangle with that same acute angle measure. So
ABC~DEF~XYZ, and BC/AC = EF/DF = YZ/XZ. These are trigonometric
radios. A trigonometric ratio is a ratio of two sides of a right
triangle. 32
Slide 4
CONFIDENTIAL4 Trigonometric Ratios DEFINITION SYMBOLS DIAGRAM A
B C a b c The sine of an angle is the ratio of the length of the
leg opposite the angle to the length of the hypotenuse. The cosine
of an angle is the ratio of the length of the leg adjacent to the
angle to the length of the hypotenuse. Next page
Slide 5
CONFIDENTIAL5 DEFINITIONSYMBOLSDIAGRAM A B C a b c The tangent
of an angle is the ratio of the length of the leg opposite the
angle to the length of the leg adjacent to the angle.
Slide 6
CONFIDENTIAL6 Trigonometric Ratios Write each trigonometric
ratio as a fraction and as a decimal rounded to the nearest
hundredth. sin R sin R = 12/13 0.92 cos R cos R = 5/13 0.38 tan R
tan R = 5/12 0.42 ~ ~ ~ ~ ~ ~ R S T 13 12 5
Slide 7
CONFIDENTIAL7 Now you try! 1) Write each trigonometric ratio as
a fraction and as a decimal rounded to the nearest hundredth. a.
cos A b. tan B c. sin B
Slide 8
CONFIDENTIAL8 Trigonometric Ratios in special Right Triangles
Use a special right to write sin 60 as a fraction. Draw and label a
30 -60 -90.
Slide 9
CONFIDENTIAL9 Now you try! 2) Use a special right triangle to
write tan 45 as a fraction.
Slide 10
CONFIDENTIAL10 Calculating Trigonometric Ratios Use your
calculator to find each trigonometric ratio. Round the nearest
hundredth. A ) cos 76 B) sin 8 C) tan 82 cos76= 0.24 sin 8= 0.14tan
82=7.12
Slide 11
CONFIDENTIAL11 Now you try! 3) Use your calculator to find each
trigonometric ratio. Round to the nearest hundredth. a. tan 11 b.
sin 62 c. cos 30
Slide 12
CONFIDENTIAL12 The hypotenuse is always the longest side of a
right triangle. So the denominator of a sine or cosine ratio is
always greater than the numerator. Therefore the sine and cosine of
an acute angle are always positive numbers less than 1. Since the
tangent of an acute angle is the ratio of the lengths of the legs,
it can have any value greater than 0.
Slide 13
CONFIDENTIAL13 Trigonometric Ratios to Find Lengths Find each
length. Round to the nearest hundredth. A) AB AB is adjacent to the
given angle, /A. You are given BC, which is opposite /A. Since the
adjacent and opposite legs are involved, use a tangent ratio. Write
a trigonometric ratio. Substitute the given values. Multiply both
sides by AB and divide by tan 41. Simplify the expression. Next
page
Slide 14
CONFIDENTIAL14 B) MP MP is opposite the given angle, /N. You
are given NP, which is the hypotenuse. Since the opposite side and
hypotenuse are involved, use a sine radio. Write a trigonometric
radio. Substitute the given values. Multiply both sides by 8.7
Simplify the expression. Next page
Slide 15
CONFIDENTIAL15 C) YZ YZ is the hypotenuse. You are given XZ,
which is adjacent to the given angle, /Z. Since the adjacent side
and hypotenuse are involved, use a cosine ratio. Write a
trigonometric ratio. Substitute the given values. Multiply both
sides by YZ and divide by cos 38. Simplify the expression.
Slide 16
CONFIDENTIAL16 NOW YOU TRY! 4) Find each length. Round to the
nearest hundredth
Slide 17
CONFIDENTIAL17 Problem Solving Application A contractor is
building a wheelchair ramp for a doorway that is 1.2 ft above the
ground. To meet ADA guidelines, the ramp will make an angle of 4.8
with the ground. To the nearest hundredth of a foot, what is the
horizontal distance covered by the ramp? Make a sketch. The answer
is BC. Write a trigonometric ratio. Substitute the given values.
Multiply both sides by BC and divide by cos 4.8. Simplify the
expression.
Slide 18
CONFIDENTIAL18 NOW YOU TRY! 5) Find AC, the length of the ramp
in Example 5. to the nearest hundredth of a foot
Slide 19
CONFIDENTIAL19 Now some practice problems for you!
Slide 20
CONFIDENTIAL20 Write each trigonometric ratio as a fraction and
as a decimal rounded to the nearest hundredth. 1)sin C 2) tan A 3)
cos A Assessment
Slide 21
CONFIDENTIAL21 Use a special right triangle to write each
trigonometric ratio as a fraction. 4) cos 60 5) tan 30 6) sin
45
Slide 22
CONFIDENTIAL22 Use your calculator to find each trigonometric
ratio. Round to the nearest hundredth. 7) tan 67 8) sin 23
Slide 23
CONFIDENTIAL23 Find each length. Round to the nearest
hundredth. AB
Slide 24
CONFIDENTIAL24 Lets review Trigonometric Ratios By the AA
Similarity Postulate, a right triangle with a given acute angle is
similar to every other right triangle with that same acute angle
measure. So ABC~DEF~CYZ, and BC/AC = EF/DF = YZ/XZ. These are
trigonometric radios. A trigonometric ratio is a ratio of two sides
of a right triangle. 32
Slide 25
CONFIDENTIAL25 Trigonometric Ratios DEFINITION SYMBOLS DIAGRAM
A B C a b c The sine of an angle is the ratio of the length of the
leg opposite the angle to the length of the hypotenuse. The cosine
of an angle is the ratio of the length of the leg adjacent to the
angle to the length of the hypotenuse. Next page
Slide 26
CONFIDENTIAL26 DEFINITIONSYMBOLSDIAGRAM A B C a b c The tangent
of an angle is the ratio of the length of the leg opposite the
angle to the length of the leg adjacent to the angle.
Slide 27
CONFIDENTIAL27 Calculating Trigonometric Ratios Use your
calculator to find each trigonometric ratio. Round the nearest
hundredth. A cos 76 B sin 8 C tan 82
Slide 28
CONFIDENTIAL28 The hypotenuse is always the longest side of a
right triangle. So the denominator of a sine or cosine ratio is
always greater than the numerator. Therefore the sine and cosine of
an acute angle are always positive numbers less than 1. Since the
tangent of an acute angle is the ratio of the lengths of the legs,
it can have any value greater than 0.
Slide 29
CONFIDENTIAL29 Trigonometric Ratios to Find Lengths Find each
length. Round to the nearest hundredth. A. AB AB is adjacent to the
given angle, /A. You are given BC, which is opposite /A. Since the
adjacent and opposite legs are involved, use a tangent ratio. Write
a trigonometric ratio. Substitute the given values. Multiply both
sides by AB and divide by tan 41. Simplify the expression.
Slide 30
CONFIDENTIAL30 Problem Solving Application A contractor is
building a wheelchair ramp for a doorway that is 1.2 ft above the
ground. To meet ADA guidelines, the ramp will make an angle of 4.8
with the ground. To the nearest hundredth of a foot, what is the
horizontal distance covered by the ramp? Make a sketch. The answer
is BC. Write a trigonometric ratio. Substitute the given values.
Multiply both sides by BC and divide by cos 4.8. Simplify the
expression.
Slide 31
CONFIDENTIAL31 Trigonometric Ratios in special Right Triangles
Use a special right to write sin 60 as a fraction. Draw and label a
30 -60 -90.