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Right Triangle Trigonometry
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The problems in this section require students to solve a right
triangle to find one or more missing parts. Although other solution
methods can often be found, the use of trigonometry is appropriate.
Some problems can be solved using the law of sines or law of cosines, but their use is not required.
- Related Resources
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Interactive resources from our Math Tools project:
Geometry: Right Triangle Trigonometry
The closest match in our Ask Dr. Math archives:
High School: Trigonometry
NCTM Standards:
Geometry Standard for Grades 9-12
Access to these problems requires a Membership.
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Arc to Area
- Annie Fetter
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Geometry, difficulty level 4. Given an arc with a measure of 40 degrees whose endpoints are at (1,5) and (5,3), find the area of the circle that contains the arc.
... more>>
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Building a Dog Enclosure
- Annie Fetter
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Geometry, difficulty level 3. Two people are arguing about whether three sections of fencing 6, 8, and 10 feet long will enclose more or less area than three sections 6, 8, and 12 feet long.
... more>>
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The Corner Banking of the Daytona Speedway
- Annie Fetter
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Geometry, difficulty level 2. Compare the corner banking at the Daytona Speedway, which is 31 degrees, with the roof on the house and garage that I helped build.
... more>>
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Drawing a Kite Plan
- Annie Fetter
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Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
... more>>
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Extending the Signals
- Lisa Lavelle
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Trig/Calc, difficulty level 1. Determine how far Erin needs to "rotate" to signal Joey at his cousin's house.
... more>>
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Field of View
- Annie Fetter
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Geometry, difficulty level 2. Figure out the field of view for two different pairs of binoculars.
... more>>
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Go Fly a Kite!
- Annie Fetter
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Geometry, difficulty level 2. If you're flying a kite 75 yards away from 70 foot tall trees, how much line would it take to get to the top of the trees? What if the kite moved up so that was 65 yards away? What would the angle be? And more!
... more>>
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Measuring the Matterhorn
- Annie Fetter
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Geometry, difficulty level 2. Use some right triangle trigonometry to calculate the height of the
Matterhorn at Disneyland.
... more>>
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The Perimeter of an Octagon
- Annie Fetter, with thanks to the Texas Education Agency
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Geometry, difficulty level 3. What's wrong with this picture of a regular octagon? Can you fix
what's wrong and find the perimeter?
... more>>
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Simple Signals
- Lisa Lavelle
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Trig/Calc, difficulty level 1. Determine the distance between Erin and Joey as well as how far Joey has travelled in "Perpendicular City."
... more>>
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Spring Up, Fall Back
- Annie Fetter
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Geometry, difficulty level 2. Help build a new rail for these solar panels so that they can be set
at three different angles.
... more>>
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Taking Pictures of the Earth
- Annie Fetter
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Geometry, difficulty level 4. If you wanted to go out into space and take a picture of the earth, how far from the earth would you have to go to make sure that you got 1/4 of the equator in your picture? How about 1/3?
... more>>
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Talladega Afternoons
- Annie Fetter
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Geometry, difficulty level 1. Compare the corner banking of a track to the steepness of the roof of
a house.
... more>>
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