Theorems & Formulas
Basic Trig
Area and Perimeter
Calculations
Transformations and Miscellaneous
100
What is this theorem called: c2 =a2 + b2?
Pythagoras' or Pythagorean Theorem
100
Two angles in a triangle are 72 degrees and 47 degrees respectively, what is the missing measurement?
61 degrees
100
A rectangular field has a diagonal length of 13 meters and one side that measures 5 meters. What is the perimeter?
13.93 or 13.928
100
Find distance of (-2,3) and (-7,7).
6.403
100
Point A (7,-13) is dilated by 3 and then reflected over the x axis. State the new coordinate.
A' = (21, 39)
200
What is the midpoint formula?
200
What is the geometric mean of 6 and 9?
7.35 OR 3 root 6
200
A right triangle has base 16m and height 11m. Find the area AND the perimeter.
PERIMETER: 46.42m or 46.416m
Area: 88 m2
200
Find Midpoint of (-4,4), (5,-1)
(0.5, 1.5)
200
Point C (4,-3) is translated right by 4 and up by 5. It is then Dilated with a scale factor of 0.5 and rotated 180 degrees. What is the new coordinate?
R180 D0.5 T(4,5) (4,-3)
Point C' = (-4,-1)
300
State the Formula that is used to calculate the length of a line on the coordinate plane given two points.
The distance formula:
300
A wire is stretched from the top of a 12-foot pole to a point on the ground that is 5 feet away from the base of the pole. How long is the wire?
13 ft
300
A trapezoid has bases of 28cm and 47cm respectively, if the height of the trapezoid is 12cm what is the area of the trapezoid?
Area: 450cm2
300
In triangle ABC, A=70, B=45 and side a=7cm find side b.
7.8cm
300
A quadrilateral has the following properties:
Both pairs of opposite sides are parallel
All four sides are equal in length
All angles are 90°
What type of quadrilateral is it?
SQUARE
400
What is the Sine Rule?
a/sinA =b/sinB=c/SinC
400
A triangular garden has base of 10meters and a height of 6 meters. What is the area of the garden?
30m2
400
An Isosceles trapezoid has base lengths of 79 and 52 respectively and a height of 17.9. Find the perimeter.
The perimeter is 175.84 units
400
In triangle ABC, side a = 12 cm, side b = 9 cm, and angle A = 48°. Find angle B and Angle C.
<B: 33.9 degrees
<C: 98.1 degrees
400
Given a 45-45-90 triangle where the base is of length 7cm what is the measurement of the hypotenuse?
7 root 2 or 9.8995/9.9
500
What other formula except the Law of sines (sine rule) can be used to find the missing side or angle of a non-right angle triangle?
Hence state the formula.
Law of Cosines or Cosine rule
a2=b2+c2-2bcCosA
500
A ladder is leaning against a wall and makes an angle of 35° with the ground. The foot of the ladder is 12 feet away from the base of the wall. How long is the ladder?
Hypotenuse:
14.65
500
A right triangle is drawn on the coordinate plane. Line AB is the height and line AC is the base. Using the distance formula calculate the area of the triangle if the vertices are:
A(1,2) B(1,15) and C(10,2).
Area is 58.5 squared units
500
In triangle ABC, side b = 14 cm, side c = 9 cm, and angle A = 60°.
Find the length of side a.
12.29cm
Law of cosines
500
Given that a 30-60-90 triangle has a base/short leg measure of 6 cm calculate the perimeter of the triangle.
28.39/28.4
Radical form: 18+6 root 3