Holt McDougal Algebra 2 Right-Angle Trigonometry Holt Algebra 2Holt McDougal Algebra 2 How do we...
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Holt McDougal Algebra 2 Right-Angle Trigonometry Right-Angle Trigonometry Holt Algebra 2 Holt McDougal Algebra 2 • 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?
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Transcript of Holt McDougal Algebra 2 Right-Angle Trigonometry Holt Algebra 2Holt McDougal Algebra 2 How do we...
Holt McDougal Algebra 2
Right-Angle TrigonometryRight-Angle Trigonometry
Holt Algebra 2Holt McDougal Algebra 2
• 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?
Holt McDougal Algebra 2
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 sine, cosine, and tangent functions for θ.
sin θ =
cos θ =
tan θ =
opp.hyp.
adj.
Holt McDougal Algebra 2
Right-Angle Trigonometry
Finding Trigonometric Ratios
2. Find the value of the sine, cosine, and tangent functions for θ.
sin θ =
cos θ =
tan θ =
opp.
hyp.adj.
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.
°
2x = 74
Which function relates the opposite and the hypotenuse?
Solve for x.
Substitute for sin 30°.
Substitute 30° for θ, x for opp, and 74 for hyp.
opp.
hyp.
x = 37
Holt McDougal Algebra 2
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?
opp.
hyp.
Substitute 45 for θ, x for opp, and 20 for hyp.
°°
Substitute for sin 45°.
Solve for x.2202 x
Holt McDougal Algebra 2
Right-Angle Trigonometry
Make sure that your calculator is set to interpret angle values as degrees. Press DRG. Check that Degree and not Radian is highlighted.
Caution!
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.
opp.
adj.
Because x is on bottom, divide.o38tan
42x o38
42
x
Substitute 38 for θ, 42 for opp., and x for adj.
Which function relates the opposite and the adjacent?
x
4238tan o
76.53x
Holt McDougal Algebra 2
Right-Angle Trigonometry
Finding Side Lengths of Other Right Triangles
6. Use a trigonometric function to find the value of x.hyp.
adj.
Because x is on top, multiply.
o52cos155x
o52 155x
Substitute 52 for θ, x for adj., and 155 for hyp.
Which function relates the adjacent and the hypotenuse?
15552cos o x
43.95x
hyp
adjcos
Holt McDougal Algebra 2
Right-Angle Trigonometry
Lesson 10.1 Practice A
