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 = πr^{2}

**Perimeter**

Rectangle : p = 2(w+h)

Triangle : p = a+b+c

Circle : c = 2πr [circumference]

**Surface Area**

Cube : a = 6w^{2}

Prism : a = 2w·d+2d·h+2w·h

Sphere : 4πr^{2}

Cylinder : 2π(r^{2}+r·h)

Cone : πr(r+√`r`^{2}+h^{2})

**Volume**

Cube : a = w^{3}

Prism : a = w·d·h

Sphere : (4/3)πr^{3}

Cylinder : πr^{2}h

Cone : (1/3)πr^{2}h

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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