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Right Triangle Trigonometry

Day 1

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Warm up

Find the missing values for the following right triangles

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Dr. Gladys West

Dr. Gladys West received an undergraduate and graduate degree in mathematics. Her accomplishments laid the groundwork for the invention of one of the most important modern day inventions, the global positioning system (GPS).

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Group roles

  • Coach
  • Accountability manager
  • Skeptic
  • Team Captain

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Raise your hand if your role fits the following description

  • I make sure that one person does not do all the work for our group.
  • I make sure that everyone is able to explain our group’s ideas.
  • I ask my group members if they have any questions that only Miss Sam can help with.
  • I make sure that my group members are thinking about our topic on a deeper level.
  • I make sure that my group works well together and participates in the activity.

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What do you notice and wonder about these ramps?

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Task: How can we make ramps safe and accessible?

  • What makes a ramp safe?
  • What do safe ramps look like?
  • What is ramp length?

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Ramp length

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Task: Which ramp is safer?

Two city planners are proposing a new ramp for a local elementary school. The school has three stairs that are 8 inches tall each. How many feet tall does the ramp have to be?

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Task: Which ramp is safer?

Two city planners are proposing a new ramp for a local elementary school. The school has three stairs that are 8 inches tall each. The ramp has to be 2 feet tall.

The first city planner, Jack Harlow, says the ramp should be 4 feet long.

The second city planner, Rihanna, says the angle between the ramp and the ground should be 45 degrees.

Is Jack Harlow’s or Rih Rih’s ramp safer? Why?

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Exit Ticket

  • What made your group role work well?
  • Did your group face any challenges in completing this task?
    • Examples: were group roles followed? Did one person do more/less than others? Did the roles feel silly?
  • What would have helped you solve the problem quicker?
    • Example: More information, mathematical equations, etc.

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Trigonometry

Day 2

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What is trigonometry?

  • The branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

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Side Ratios

  • Used to measure the angles and sides of a right angle triangle
  • 3 major values:
    • Sine (sin)
    • Cosine (cos)
    • Tangent (Tan)
  • Radians: An angle whose corresponding arc in a circle is equal to the radius of the circle

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Side Ratios

  • Sine
  • Cosine
  • Tangent

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Here’s a little jingle

Video here

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Practice

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Unit Circle

  • A circle on the Cartesian Plane that has a radius of 1 unit and is centered at the origin (0, 0).
  • The unit circle is a powerful tool that provides us with easier reference when we work with trigonometric functions and angle measurements.
  • You can apply the Pythagorean Theorem to the unit circle.

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Right Triangle Trigonometry

Day 3

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Warm up

Find:

  1. Sin A

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  • Cos A

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  • Tan C

A

B

C

12

18

16

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How to find angle measurements from side lengths

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How to find angle measurements from side lengths

72

97

65

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Taking the inverse of a trig function

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What if you only have 2 side lengths?

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What if you only have 2 side lengths?

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Practice :)

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Reminders!

  • Notebook check FRIDAY!
    • Make sure you have worksheets completed and have caught up on days missed
  • Visit the tutoring center
    • Monday, Tuesday, Thursday, Friday
    • I can print worksheets, practice problems, notes for extra practice!

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Right Triangle Trigonometry

Day 4

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Warm up: Find the angle measurement

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Laws of Sines

  • Can be used to solve side lengths or angle measurements for any kind of triangle!
  • Used to solve a triangle when:
    • When we know two angles and one side
    • When we know two angles and one side
    • When we can use ASA or AAS

https://www.youtube.com/watch?v=VjmFKle7xIw

https://www.youtube.com/watch?v=yC0Dmbge8Xs

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Activity: Coloring by Trigonometry

  • Practice finding angle measurements with two given sides!

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Right Triangle Trigonometry

Day 5

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Warm up

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Law of Sines

  • Can be used to solve side lengths or angle measurements for any kind of triangle!
  • Used to solve a triangle when:
    • When we know two angles and one side
    • When we know two angles and one side
    • When we can use ASA or AAS

https://www.youtube.com/watch?v=VjmFKle7xIw

https://www.youtube.com/watch?v=yC0Dmbge8Xs

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