On this page you will find some material about Lesson 26. Read through the material below, watch the videos, and follow up with your instructor if you have questions.
Lesson 26: Solving Right Triangles & Applications of Static Trigonometry
Learning Outcomes. (from Coburn and Herdlick’s Trigonometry book)
- Solve a right triangle given one angle and one side.
- Solve a right triangle given two sides.
- Solve applications involving angles of elevation and depression.
- Solve applications involving angles of rotation.
- Solve general applications of right triangles.
Topic. This lesson covers
Section 2.2: Solving Right Triangles, and
Section 2.3: Applications of Static Trigonometry.
WeBWorK. There are two WeBWorK assignments on today’s material:
Video Lesson 26 – part 1 (based on Lesson 26 Notes – part 1)
Video Lesson 26 – part 2 (based on Lesson 26 Notes – part 2)
These are questions on fundamental concepts that you need to know before you can embark on this lesson. Don’t skip them! Take your time to do them, and check your answer by clicking on the “Show Answer” tab.
If you are not comfortable with the Warmup Questions, don’t give up! Click on the indicated lesson for a quick catchup. A brief review will help you boost your confidence to start the new lesson, and that’s perfectly fine.
Need a review? Check Lesson ??
This is like a mini-lesson with an overview of the main objects of study. It will often contain a list of key words, definitions and properties – all that is new in this lesson. We will use this opportunity to make connections with other concepts. It can be also used as a review of the lesson.
A Quick Intro to Solving Right Triangles & Applications of Static Trigonometry
Key Words. Right angle, hypotenuse, leg, opposite leg, adjacent leg, Pythagorean Theorem, sine, cosine, tangent, cosecant, secant, cotangent, arcsine, arccosine, arctangent, solving a right triangle, special triangle, 30-60-90, 45-45-90, angle of depression and angle of elevation.
A right angle is an angle that measures .
A right triangle is a triangle with a right angle.
The sum of the angles in a triangle is .
Pythagorean Theorem: In a right triangle, if the legs measure and and the hypotenuse measures , then
Arcsine: if , then
Arccosine: if , then
Arctangent: if , then
Solving a right triangle means to find the unknown angles and sides.
Special Triangle: This is a triangle whose angles are , and . This triangle is special, because the sides are in a special proportion. If the short leg (the opposite leg to ) is , then
Special Triangle: This is a triangle whose angles are , and . This triangle is special, because the sides are in a special proportion. If the legs are , then
The angle made by the line of sight of an observer on the ground to a point above the horizontal is called the angle of elevation.
The angle made by the line of sight of an observer above to a point on the ground is called the angle of depression.
Many times the mini-lesson will not be enough for you to start working on the problems. You need to see someone explaining the material to you. In the video you will find a variety of examples, solved step-by-step – starting from a simple one to a more complex one. Feel free to play them as many times as you need. Pause, rewind, replay, stop… follow your pace!
A description of the video
In this video you will see the following problem:
A helicopter is flying 1,000 ft over a building. The pilot spots a person with an angle of depression . How far is the person from the building?
Now that you have read the material and watched the video, it is your turn to put in practice what you have learned. We encourage you to try the Try Questions on your own. When you are done, click on the “Show answer” tab to see if you got the correct answer.
You should now be ready to start working on the WeBWorK problems. Doing the homework is an essential part of learning. It will help you practice the lesson and reinforce your knowledge.
It is time to do the homework on WeBWork:
When you are done, come back to this page for the Exit Questions.
After doing the WeBWorK problems, come back to this page. The Exit Questions include vocabulary checking and conceptual questions. Knowing the vocabulary accurately is important for us to communicate. You will also find one last problem. All these questions will give you an idea as to whether or not you have mastered the material. Remember: the “Show Answer” tab is there for you to check your work!
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