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August 23, 2014

August 23, 2014

Posted by **Sammie** on Tuesday, June 17, 2008 at 9:53pm.

1. Find the radius of the circle with the given measurement.

C=7

2. Find the value of x using the special triangles (30-60-90).

I really don't get this concept. Will someone explain it to me?

3. Use the coordinates A (-3, -7) and B (1, -5).

Find the distance of AB

Find the midpoint of AB

4. The length of a diagonal of a rectangular prism is 4√15. If the dimensions of the base are 8 and 12, then find the altitude.

5. Consider the coordinates A (12, 5, -5) and B (12, -3, -5). Find the volume of the spatial figure formed by rotating AB about the y-axis.

- Geometry -
**Reiny**, Tuesday, June 17, 2008 at 10:46pm1. Is C=7 supposed to mean Circumference = 7?

If so, C = 2pi(r)

7 = 2pi(r)

r = 7/2pi

= appr. 1.114

2. In the 30-60-90 right-angled triangle, the sides are in the ration 1 : √3 : 2 for the sides across from the corresponding angles.

So If you are given any of the sides, you can set up a ratio.

e.g. suppose the side across from the 60º angle is 12 cm, then

for the hypotenuse h,

h/x = 12/√3

h = 24/√3

3. According to the formula for AB, which you should definitely know for the test,

AB = √[(-5+7)^2 + (1+4)^2]

= √29

Midpoint ?? One of the most basic of the fundamental geometry formulas

midpoint = ((-3+1)/2 , (-7-5)/2)

= (-1,-6)

4. Let the altitude be h

then h^2 + 8^2 + 12^2 = (4√15)^2

solve for h

5. I can visualize a cylinder with a height of 8 (the difference in the y-values), and a radius of √(12^2 + (-5)^2)

= 13

so volume = pi(r^2)h

= pi(169)(8)

= appr. 4247.4 units^3

AB =

- Geometry -
**Reiny**, Tuesday, June 17, 2008 at 10:48pmI just notice a typo in #3

h/x = 12/√3 should say h/2 = 12/√3

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