right triangle triginometry
DESCRIPTION
Right Triangle Triginometry. A Stand- Alone Instructional Resource. Created by Lindsay Sanders. Standards & Objectives. Students in Mathematics II will be able to- Discover the relationship of the trigonometric ratios for similar triangles. - PowerPoint PPT PresentationTRANSCRIPT
Right Triangle TriginometryA Stand-Alone Instructional Resource
Created by Lindsay Sanders
Standards & Objectives
Students in Mathematics II will be able to-• Discover the relationship of the trigonometric
ratios for similar triangles.• Explain the relationship between the
trigonometric ratios of complementary angles.• Solve application problems using the
trigonometric ratios.
Introduction• This project is a tutorial for learning how to solve
right triangles using basic trigonometry.• You will learn vocabulary, participate in mini-
lessons, and answer questions based on what you learned.
• You will need a scientific calculator or use an online scientific calculator
• At the end of this tutorial, there are links to online resources for right triangle trigonometry, including applets and games.
Vocabulary
• Hypotenuse- the longest side, opposite of the right angle
• Opposite side- the side opposite of the chosen angle
• Adjacent side- the side touching the chosen angle
hypotenuse
adjacent
opposite To learn more, please watch this video
Trigonometric Ratios
Sine Cosine
Tangent
Click on the trigonometric ratios below to learn more.
Sine• A trigonometric ratio (fraction) for acute angles that
involve the length of the opposite side and the hypotenuse of a right triangle, abbreviated Sin
length of hypotenuse ABSin A = =
A
B
C
opposite
hypotenuseClick for example
Click fortrig ratios
length of leg opposite A BC
Example 1Find Sin A.
A
B
C
2515
20
Sin A = =hypotenuseBC
Click fortrig ratios
=15
25
= 35
= 0.60
oppositeAB
Click forpractice
You try!Find Sin A.
A
B
C
53
45
28
Click fortrig ratios
Click foranother
(a) = 0.62 2845
(b) = 0.532853
(c) = 0.85 4553
(d) = 1.89 5328
No this ratio is opposite over adjacent
No this ratio is adjacent over hypotenuse
No this ratio is hypotenuse over opposite
Yes this ratio is opposite over hypotenuse
Back to example
You try!Find Sin B.
A
B
C
24 26
10
Click fortrig ratios
(a) = 0.42 1024
(b) = 0.92 2426
(c) = 2.40 2410
(d) = 0.391026
No this ratio is opposite over adjacent
No this ratio is adjacent over opposite
No this ratio is adjacent over hypotenuse
Yes this ratio is opposite over hypotenuse
Back Click forCosine
Cosine• A trigonometric ratio for acute angles that involve
the length of the adjacent side and the hypotenuse of a right triangle, abbreviated Cos
length of hypotenuse ABCos A = =
A
B
C adjacent
hypotenuseClick for example
Click fortrig ratios
length of leg adjacent A AC
Example 2Find Cos A.
A
B
C
2515
20
Cos A = =hypotenuse
25
Click fortrig ratios
=20
AB
=54
= 0.80
adjacent AC
Click forpractice
You try!Find Cos A.
A
B
C
37 35
12
Click fortrig ratios
(a) = 0.32 1237
(b) = 0.95 3537
(c) = 2.92 3512
(d) = 0.341235
No this ratio is adjacent over opposite
No this ratio is opposite over adjacent
No this ratio is opposite over hypotenuse
Yes this ratio is adjacent over hypotenuse
Back to example
Click foranother
You try!Find Cos B.A
B
C
85
36
77
Click fortrig ratios
(a) = 0.42 3685
(b) = 0.47 3677
(c) = 0.91 7785
(d) = 1.108577
No this ratio is hypotenuse over adjacent
No this ratio is opposite over hypotenuse
No this ratio is opposite over adjacent
Yes this ratio is adjacent over hypotenuse
Back Click forTangent
Tangent• A trigonometric ratio for acute angles that involve
the length of the opposite side and the adjacent side of a right triangle, abbreviated Tan
length of leg adjacent ACTan A = =
A
B
C adjacent
Click for example
opposite
Click fortrig ratios
length of leg opposite A BC
Example 3Find Tan A.
A
B
C
2515
20
Tan A = = adjacent
=
Click fortrig ratios
AC
2015
=43
= 0.75
opposite BC
Click forpractice
Back
You try!Find Tan A.
A
BC
58
40
42
Click fortrig ratios
(a) = 1.05 4240
(b) = 0.72 4258
(c) = 0.69 4058
(d) = 0.954042
No this ratio is opposite over hypotenuse
No this ratio is adjacent over opposite
No this ratio is adjacent over hypotenuse
Yes this ratio is opposite over adjacent
Back Click foranother
You try!Find Tan B.
A
B
C12
915
Click fortrig ratios
(a) = 1.33 12 9
(b) = 0.60 915
(c) = 0.801215
(d) = 0.75 912
No this ratio is opposite over hypotenuse
No this ratio is adjacent over opposite
No this ratio is adjacent over hypotenuse
Yes this ratio is opposite over adjacent
Back Click to go on
Solving for a Side Length
In order to solve for x, you will need to use one of the trigonometric ratios you just learned about!
52x
42˚Click fortrig ratios
Click for example
Example 4Solve for x.
52x
42˚
Step 1. Decide what type of sides are given.
x – opposite52 – hypotenuse
Step 2. Decide what trig function to use.
Sine! It is opposite over hypotenuse!
Step 3. Set up the ratio and solve for x.
Sin 42˚ =
x
52Multiply both side by 52· 5252 ·Put 52 · sin 42 in calculator
34.8 = x
Click forpractice
Click fortrig ratios
Back
You try!Solve for x.
16
x
39˚
Click foranswer
Click fortrig ratios
Back
x = 10.1answer:
Click foranother
Click fortrig ratios
Back
You try!Solve for x.
10
x
31˚
Click foranswer
Click fortrig ratios
Back
x = 8.6answer:
Click foranother
Click fortrig ratios
Back
You try!Solve for x.
23
x
44˚
Click foranswer
Click fortrig ratios
Back
x = 22.2answer:
Click formore
Click fortrig ratios
Back
For more information…
@Home Tutor – Right Triangle Trig
YourTeacher – Solving for sides using Trig video
Right Triangle Calculator and Solver
This Stand Alone Instructional Resource was created using PowerPoint. All sounds are also from PowerPoint. Information, definitions, and examples
were adapted from in McDougall Littell’s Mathematics 2 textbook. Click to start over