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Geometry

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I have several questions, because my geometry final is tomorrow. I've completed most of the review, but can't seem to figure out these questions. It would be great if someone could tell me how to solve each equation.

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 -

    1. 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 -

    I just notice a typo in #3

    h/x = 12/√3 should say h/2 = 12/√3

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