Transcript Holt McDougal Algebra 2

Right-Angle
Right-AngleTrigonometry
Trigonometry
• How do we understand and use
trigonometric relationships of acute
angles in triangles?
• How do we determine side lengths of
right triangles by using trigonometric
functions?
HoltMcDougal
Algebra 2Algebra 2
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Right-Angle Trigonometry
A trigonometric function is a function whose rule is
given by a trigonometric ratio. A trigonometric ratio
compares the lengths of two sides of a right triangle. The
Greek letter theta θ is traditionally used to represent the
measure of an acute angle in a right triangle. The values
of trigonometric ratios depend upon θ.
Holt McDougal Algebra 2
Right-Angle Trigonometry
Holt McDougal Algebra 2
Right-Angle Trigonometry
Finding Trigonometric Ratios
1. Find the value of the
opp.
sine, cosine, and
tangent functions for θ.
hyp.
adj.
sin θ =
cos θ =
tan θ =
Holt McDougal Algebra 2
Right-Angle Trigonometry
Finding Trigonometric Ratios
2. Find the value of the
adj.
sine, cosine, and
tangent functions for θ.
hyp.
opp.
sin θ =
cos θ =
tan θ =
Holt McDougal Algebra 2
Right-Angle Trigonometry
You will frequently need to determine the value of
trigonometric ratios for 30°,60°, and 45° angles as
you solve trigonometry problems. Recall from
geometry that in a 30°-60°-90° triangle, the
ration of the side lengths is 1: 3 :2, and that in a
45°-45°-90° triangle, the ratio of the side lengths is
1:1: 2.
Holt McDougal Algebra 2
Right-Angle Trigonometry
Holt McDougal Algebra 2
Right-Angle Trigonometry
Finding Side Lengths of Special Right Triangles
3. Use a trigonometric function to find the value of x.
Which function relates
the opposite and the
hypotenuse?
°
Substitute 30° for θ, x
for opp, and 74 for hyp.
Substitute
2x = 74
x = 37
Holt McDougal Algebra 2
hyp.
Solve for x.
for sin 30°.
opp.
Right-Angle Trigonometry
Finding Side Lengths of Special Right Triangles
4. Use a trigonometric function to find the value of x.
Which function relates
the opposite and the
hypotenuse?
°
Substitute 45° for θ, x
for opp, and 20 for hyp.
Substitute
2 x  20 2
Holt McDougal Algebra 2
Solve for x.
for sin 45°.
hyp.
opp.
Right-Angle Trigonometry
Caution!
Make sure that your calculator is set to interpret
angle values as degrees. Press DRG. Check that
Degree and not Radian is highlighted.
Holt McDougal Algebra 2
Right-Angle Trigonometry
Finding Side Lengths of Other Right Triangles
5. Use a trigonometric function to find the value of x.
42
tan 38 
x
42
x
o
tan 38
o
x  53.76
Holt McDougal Algebra 2
Which function
relates the opposite
and the adjacent?
Substitute 38 for θ, 42
for opp., and x for adj.
42
opp.
Because x is on bottom,
divide.
38 o
x
adj.
Right-Angle Trigonometry
Finding Side Lengths of Other Right Triangles
6. Use a trigonometric function to find the value of x.
adj
cos  
hyp
Which function
o
52
x
relates the adjacent
and the hypotenuse? adj.
x
cos 52 
155
Substitute 52 for θ, x for
adj., and 155 for hyp.
x  155 cos 52
Because x is on top,
multiply.
o
x  95.43
Holt McDougal Algebra 2
o
hyp.
155
Right-Angle Trigonometry
Lesson 10.1 Practice A
Holt McDougal Algebra 2