Math Forum - Problems Library - Geometry - Special Right Triangles

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right triangles
Pythagorean theorem
special right triangles
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Geometry
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Special Right Triangles
Problems in this category contain a 30-60-90 or a 45-45-90 special right triangle.

Related Resources
Interactive resources from our Math Tools project:
   Geometry: Special Right Triangles
The closest match in our Ask Dr. Math archives:
   High School: Triangles
NCTM Standards:
   Geometry Standard for Grades 9-12


Access to these problems requires a Membership.

Building a Regular Hexagon - Annie Fetter and Steve Weimar
Geometry, difficulty level 3. How do you form a regular hexagon by attaching rectangles to the sides of an equilateral triangle? ... more>>

Building a Vaulted Ceiling - Annie Fetter
Geometry, difficulty level 4. An eyebrow window is a 15-inch-deep slice off an 8.5-foot circle. How wide will the base of the window be? ... more>>

Diagonal Dilemma - Karen Cohen
Geometry, difficulty level 1. What is the area of the square ABCD that has a diagonal of length 12 cm? ... more>>

Equilateral Triangle and Square Ratio - Dale Pearson
Geometry, difficulty level 3. A square with side length s is inscribed in an equilateral triangle of side length t. Find the ratio t/s. ... more>>

Examining an Octagon - Annie Fetter
Geometry, difficulty level 3. Describe the rectangles that you would need to put on the sides of a square in order to be able to end up with a regular octagon when you connect the outside vertices of the figure. ... more>>

Finding the Base of a Trapezoid - Annie Fetter
Geometry, difficulty level 3. Given trapezoid ABCD, with AD one base and BC the other and a 60 degree angle at CDA. If CD is 26sqrt3/3 meters, BC is 7 meters, and the area of the trapezoid is 130 square meters, what's the length of AD? ... more>>

The Length of a Belt - Annie Fetter
Geometry, difficulty level 3. The diameters of two wheels are 18 cm and 12 cm and their centers are 30 cm apart. A belt goes around them and crosses 18 cm from the center of the big wheel. How long is the belt? How do you know you're right? ... more>>

A Minor Arc Subtended by a What?? - Annie Fetter
Geometry, difficulty level 2. A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are radii of the circle. The length of the chord is 6 times the square root of 2. What is the length of the minor arc subtended by the chord? ... more>>

More Tangents! - Annie Fetter
Geometry, difficulty level 3. Given a square ABCD inscribed in a unit circle. AB is extended to P, where PC is tangent to the circle. Find the length of PD. ... more>>

Nautical Navigation - Annie Fetter
Geometry, difficulty level 2. Help the sailors of the Kaleidoscope figure out what time they'll pass the lighthouse and how far from the lighthouse they'll be at that time. ... more>>

Olympic Softball - Annie Fetter
Geometry, difficulty level 2. Should the pitcher's rubber in Olympic softball be behind the line drawn from third base to first base, or in front of it? ... more>>

A Quickie Triangle Puzzle - Sasha Sokolsky
Geometry, difficulty level 2. Find the length of the unknown side of this triangle using knowledge of special right triangles. ... more>>

Snail's Trail - Annie Fetter, Lillian Ray
Geometry, difficulty level 2. What should be the dimensions of the smallest piece of my "Snail's Trail" quilt? ... more>>

The Subtending Chord - Annie Fetter
Geometry, difficulty level 3. A chord of a circle is the hypotenuse of an isosceles right triangle whose legs are radii of the circle. The length of the chord is 8 times the square root of 2. What is the length of the minor arc subtended by the chord? ... more>>

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? ... more>>

TV Dimensions - Annie Fetter
Geometry, difficulty level 2. If the aspect ratio of a TV is 16:9 and the diagonal measures 50 inches, what are the dimensions of the screen? ... more>>

What Do We Know About Tangents? - Annie Fetter
Geometry, difficulty level 2. Given two externally tangent congruent circles, construct a segment from the center of one circle tangent to the other circle. If the length of this segment is 10, what's the radius of the circles? ... more>>

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