Geo
Finding C
One of the most famous mathematicians who has ever lived, Pythagoras, a Greek scholar who lived way back in the 6th century B.C. (back when Bob Dole was learning geometry), came up with one of the most famous theorems ever, the Pythagorean Theorem. It says - in a right triangle, the square of the measure of the hypotenuse equals the sum of the squares of the measures of the two legs. This theorem is normally represented by the following equation: a2 + b2 = c2, where c represents the hypotenuse.
With this theorem, if you are given the measures of two sides of a triangle, you can easily find the measure of the other side.
Example
1. Problem: Find the value of c.
Accompanying Figure
Solution: a2 + b2 = c2 Write the Pythagorean
Theorem and then plug in any
given information.
52 + 122 = c2 The information that was
given in the figure was
plugged in.
169 = c2 Solve for c By finding the square root of the number
c = 13
2. Problem: A ladder 12 meters long leans
against a building. It rests on
the wall at a point 10 meters
above the ground. Find the angle
the ladder makes with the ground.
Solution: Make sure you know what is being
asked. Then use the given
information to draw and label a
figure.
a2+b2=c
12,2+10,2=c
c2=144+100
c=244
square root of 244 is 15.62
c=15.62
Finding A-B i will do later
FINDING B
FINDING B
FINDING B
FINDING B
FINDING B
FINDING B
SINCE ADDING SIDE A AND SIDE B GIVES YOU SIDE C, TAKE AWAY SIDE A FROM SIDE C TO GET SIDE B
OR
C² - A² = B²
WITH THAT YOU CAN THIS:
C² - A² = B²...FORMULA
10² - 6² = B²...REPLACE A & C
(10X10) - (6X6) = B²...SQUARE A & C
100 - 36 = B²
64 = B²...SUBTRACT
You then find the squre root of 68 (8x8=68) your answer is B=8
(Rainer said i could use this so thank you Rainer)
Finding A is the same thing As finding B
Geometric Formulas
Area
Rectangle : a = w·h
Triangle : a = (1/2)b·h
Circle : a = πr2
Perimeter
Rectangle : p = 2(w+h)
Triangle : p = a+b+c
Circle : c = 2πr [circumference]
Surface Area
Cube : a = 6w2
Prism : a = 2w·d+2d·h+2w·h
Sphere : 4πr2
Cylinder : 2π(r2+r·h)
Cone : πr(r+√r2+h2)
Volume
Cube : a = w3
Prism : a = w·d·h
Sphere : (4/3)πr3
Cylinder : πr2h
Cone : (1/3)πr2h
Quiz
http://www.mccc.edu/~kelld/geometry3/geometry3.htm
http://www.mccc.edu/~kelld/geometry2/Geometry2.htm
http://www.mccc.edu/~kelld/geometry1/geometry1.htm
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