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Right Triangle Trigonometry

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

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 912
Access to these problems requires a Membership.

Arc to Area
 Annie Fetter

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.
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Building a Dog Enclosure
 Annie Fetter

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.
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The Corner Banking of the Daytona Speedway
 Annie Fetter

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.
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Drawing a Kite Plan
 Annie Fetter

Geometry, difficulty level 3. Given a picture of a kite plan, figure out the radius of the circle that creates the curved section.
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Extending the Signals
 Lisa Lavelle

Trig/Calc, difficulty level 1. Determine how far Erin needs to "rotate" to signal Joey at his cousin's house.
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Field of View
 Annie Fetter

Geometry, difficulty level 2. Figure out the field of view for two different pairs of binoculars.
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Flying High
 Annie Fetter

Geometry, difficulty level 1. Figure out which of two planes is gaining altitude more quickly.
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Measuring the Matterhorn
 Annie Fetter

Geometry, difficulty level 2. Use some right triangle trigonometry to calculate the height of the
Matterhorn at Disneyland.
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The Perimeter of an Octagon
 Annie Fetter, with thanks to the Texas Education Agency

Geometry, difficulty level 3. What's wrong with this picture of a regular octagon? Can you fix
what's wrong and find the perimeter?
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Pisa's Lean
 Annie Fetter

Geometry, difficulty level 4. Explore the angle and distance at which the Leaning Tower of Pisa actually leans.
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Simple Signals
 Lisa Lavelle

Trig/Calc, difficulty level 1. Determine the distance between Erin and Joey as well as how far Joey has travelled in "Perpendicular City."
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Spring Up, Fall Back
 Annie Fetter

Geometry, difficulty level 2. Help build a new rail for these solar panels so that they can be set
at three different angles.
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Taking Pictures of the Earth
 Annie Fetter

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?
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Talladega Afternoons
 Annie Fetter

Geometry, difficulty level 1. Compare the corner banking of a track to the steepness of the roof of
a house.
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