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Special Right Triangles

Problems in this category contain a 306090 or a 454590 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 912
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 15inchdeep slice off an 8.5foot 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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