Special Right Triangles & Trigonometry
Circles
Areas and Volumes
Facts about the Teaching Fellows
100
Without using a calculator, find the sine of which angle equals cos(23°) .
sin(67°)=cos(23°)
100
If OM=25, MT=15, and OT=20, is AB tangent to Circle O? Explain.
Yes, because OM^2=MT^2+OT^2
100
Find the area of a sector with a central angle
theta=45°
in a circle of radius r=4.
A=2pi
100
Name one university where one of the Teaching Fellows went to college.
Colby College, Reed College, University of Richmond, NYU, Yale University, Hamilton College, Middlebury College, or the University of Pittsburgh.
200
Find sides x and y in the following right triangle.
x≈20.9 and y≈13.4
200
Build the equation of the circle centered at (9,-2) with a radius of 6.
(x-9)^2+(y+2)^2=36
200
Find the area of the annulus if the smaller circle has a radius of 5 and the bigger circle has a diameter of 20.
A=75pi
200
Which two Teaching Fellows teach biology?
Mr. Ahmed and Mx. Thayer
300
Find side j in the following triangles in its most simplified form.
j=7
300
In the following figure, the smaller circle has a radius of 13 and the bigger circle has a radius of r. Given that their common chord is 24 while the line segment joining their centers is 21, find r.
r=20
300
Find the area of the following segment.
A=6pi-9sqrt2
300
What are the two subjects that Ms. Manou Georgila studied in college?
Mathematics and Global Studies
400
Find all missing sides and angles in the following triangle.
\angle A≈48.2°
,
\angle B≈41.8°
and
BC=7sqrt5
400
If AD=4, FC=7, and BC=12, find the Perimeter of triangle ABC.
P=32
400
Find the surface area of the following cylinder.
SA=128pi
400
Which 4 Teaching Fellows are from Massachusetts?
Mr. Ahmed, Ms. Metzger, Ms. Sullivan, and Ms. Visco.
500
Find sides a, b, c, d, and x in the following trapezoid in their most simplified form.
a=12sqrt2, b=20 , c=4sqrt6 , d=12sqrt2 , and x=20+12sqrt2+4sqrt6
500
Find ∠PMN, ∠LNP, and ∠MNP , and arcs PN, and LN.
∠PMN=68, ∠LNP=46, ∠MNP=90, PN=136, and LN=132
500
Find the volume of the following square pyramid.
V=400
500
Name 5 dorms where the Teaching Fellows house counsel.
Chase/Isham, Johnson, Rockwell, Bishop, Foxcroft, Day, Paul Revere, or Stuart.