Trigonometry: Right Triangle Trigonometry
Contains Right Triangle Trigonometry Applets
Table of Contents
- Units of Angle/Arc Measure (Radians, Degrees)
- 1 Radian: Clear Definition
- Movie: Radians to Revs
- 3 Main Trigonometric Ratios
- Identifying Sides of Right Triangles
- Right Triangle Trigonometry: Intro
- Trigonometric Ratios (Right Triangle Context)
- Application Problems
- How Fast are You Spinning?
- Older Versions of Newer Materials
- SOH-CAH-TOA's Failure (II)
- The 3 Main Trigonometric Ratios
- True Meanings of the 3 Trigonometric Ratios within a Right Triangle Context
- 30-60-90 Triangle
1 Radian: Clear Definition
[color=#c51414]One unit of ANGLE or ARC MEASURE which you're probably familiar with is that of a "degree." One degree is 1/360th of a full revolution, right? [/color][br][color=#0a971e]Another unit of ANGLE or ARC MEASURE is a "revolution". 1 revolution = 360 degrees, right? [/color][br][br][color=#1551b5]Well, there is ANOTHER unit of ANGLE or ARC MEASURE with which you'll soon become familiar. [/color] [br][color=#1551b5]This new unit of ANGLE or ARC MEASURE is called a [b]RADIAN[/b]. [/color] [br][br][i][color=#b20ea8]Interact with the applet below for a few minutes. [br]Reset it a few times and start the animation again each time.[br]Be sure to change the circle's radius as you go along. [br][br][b][color=#1551b5]After interacting with this applet, answer the question that appears immediately below it.[/color][/b][/color] [/i]
Again, recall that a "degree", a "revolution", and a "radian" are all units of ARC MEASURE (i.e. AMOUNT OF SPIN). [br][br][color=#c51414][b]Complete the following sentence definition:[/b][/color] [br][br][b][color=#1551b5]Definition: 1 RADIAN is defined to be a unit of ARC MEASURE for which.....[/color][/b]
Identifying Sides of Right Triangles
The applet below provides an introduction as to how we label the legs of a right triangle with respect to ONE of its acute angles. (Notice angle A, B, A', and B' are acute angles of a right triangle.) [br][br]The triangles shown below are similar triangles. Can you explain why?
1) How would you describe the hypotenuse of a right triangle? What is it? How do you easily find it? [br][br]2) How, within a right triangle, would you be able to identify an acute angle's OPPOSITE LEG? [br][br]3) How, within a right triangle, would you be able to identify an acute angle's ADJACENT LEG?
How Fast are You Spinning?
Our Earth is ALWAYS spinning. Yet, j[i]ust how fast[/i] is earth rotating? [br][br]Everyone on Earth spins 360 degrees in a 24 hour period. 360 degrees / 24 hrs = 15 degrees per hour. [br]This is Earth's ANGULAR SPEED ([i]amount of rotation[/i] per [i]unit time[/i]). This remains constant. [br][br]Yet what's [b]NOT CONSTANT[/b] is one's [b]LINEAR SPEED[/b] ([i]distance traveled[/i] per [i]unit time[/i]). [br]In a 24 hour period, we all--(unless we're flying a great distance in an airplane)--"spin along" a circle of latitude. [br]Some circles of latitude are bigger than others. (Observe in the applet below.) [br]Since this is the case, we [b]CANNOT ALL HAVE the same LINEAR SPEED[/b] as every other person on the planet! [br][br][color=#1551b5][b]Let's assume Earth to be a perfect sphere [/b][/color]([i]for simplicity's sake![/i]) [br]According to NASA's website (http://solarsystem.nasa.gov/planets/profile.cfm?Display=Facts&Object=Earth), [br]Earth has a [color=#d69210][b]mean radius of 3,958.8 miles.[/b][/color] [br]To successfully answer the 2 questions in this applet, all you will need is the following: [br][br]1) [color=#b20ea8]The latitude of your location [/color][br]2) A good working knowledge of some basic geometry formulas. [br]3) A good working knowledge of basic right-triangle trigonometry. [br][br]Have fun with this! [b]([i]Don't check a checkbox before answering the question that precedes it![/i])[/b]