Geometry and Trigonometry

Triangles and Bearings

100

This two terms are the full classification of a triangle with side lengths of 6 in, 9 in, and 12 in. 

What are Obtuse and Scalene? 

200

If you are 30 feet away from two separate buildings, the angle of elevation looking up at the taller one is 60^o, and the angle of elevation looking up at the shorter one is 54^o, then this is the difference between the heights of the buildings. 

What is about 10.7 feet?

300

If the bearing of B from A is 56^o, then this is the bearing of A from B. 

What is 236^o?

400

In a triangle with a 25^o angle, a side length of 8 cm opposite from that angle, and a side length of 12 cm adjacent to that angle, this is the area.

What is about 43.3 cm²?

500

If the angle of elevation looking up at a mountain changes from 12^o to 25^o by moving 0.3 miles closer to the mountain, then this is the height of the mountain. 

What is about 0.117 miles? 

OR 

What is about 619 feet?

Circles

100

This is a line that crosses through a circle. 

What is a secant line?

200

This is the degree measure of 2π/15 radians. 

What is 24^o?

300

This is a figure formed by an arc and a chord of a circle. 

What is a segment?

400

This is the entire surface area of a hemisphere with a radius of 18 cm. 

What is 972π cm²? 

OR 

What is about 3,053.63 cm²?

500

This is area of a sector formed from a 3 inch arc and two 5 inch radii. 

What is 7.5 in²?

Polygons and Solids

100

This is a line segment in a regular polygon from a midpoint of one of its sides to its center. 

What is an apothem?

200

This is the volume of a sphere with a surface area of 196π cm². 

What is about 457.333 π cm³? 

OR 

What is about 1,436.755 cm³?

300

This is the ratio between a prism and pyramid, each with the same base and height. 

What is 3? 

OR 

What is 3:1?

400

This is the specific name of a polygon with 672 sides.(Not 672-gon). 

What is a hexahectaheptacontakaidigon?

500

If there are three spheres tightly packed in a cylinder (where the both the spheres and cylinder have the same the diameter and the spheres are stacked tightly above each other with the top and bottom spheres touching the respective base of the cylinder) then this is the percentage of the cylinder that is empty.

What is 1/3? 

Or 

What is about 33.3%?

Voronoi Diagrams

100

This is a point equidistant to at least three sites in a Voronoi diagram. 

What is a vertex?

200

In a Voronoi diagram, all edges will be parallel if the sites are this. 

What is colinear?

300

A vertex in a Voronoi diagram is the this of a triangle formed by three sites in the Voronoi diagram. 

What is the circumcenter?

400

If Site A is at (4,8) and Site B is at (10,16), then this is an equation for the edge separating the respective cells containing Sites A and B.

What is y - 12 = -3/4 (x - 7)? 

OR 

What is y = -3/4 x + 69/4?

OR 

What is y = -3/4 x + 17.25?

500

This is the vertex of a Voronoi diagram with sites at (1,5), (7,11), and (5,17).

What is (0,12)?

Trivia

100

This is the material from which Wolverine's claw is made. 

What is Adamantium? 

200

This is the process of splitting an atom's nucleus, which releases a significant amount of energy. 

What is fission?

300

This is where Lorelai Gilmore accidentally ordered three cups of coffee. 

What is Weston's Bakery?

400

This island is the inspiration for Melemele Island. 

What is O'ahu?

500

This is the total number of episodes of the television show Friends. 

What is 236?