Page 28 - Calculus Workbook For Dummies

12 Part I: Pre-Calculus Review

Geometry: When Am I Ever Going to Need It?

You can use calculus to solve many real-world problems that involve surfaces, volumes,
and shapes, such as maximizing the volume of a cylindrical soup can or determining
the stress along a cable hanging in a parabolic shape. So you’ve got to know the basic
geometry formulas for length, area, and volume. You also need to know basic stuff like
the Pythagorean Theorem, proportional shapes, and basic coordinate geometry like the
distance formula.

Q. What’s the area of the triangle in the fol- Q. How long is the hypotenuse of the triangle
lowing figure? in the previous example?

A. x = 4
2
2
a + b = c 2
x 3 x = a + b 2
2
2
2 2
2
x = 13 + 3
2
x = 13 + 3
2
13 x = 16
x = 4
A. 39
2
1
$
Area triangle = base height
2
1
= $ 13 3
2
39
=
2
17. Fill in the two missing lengths for the sides 18. What are the lengths of the two missing
of the triangle in the following figure. sides of the triangle in the following figure?

10
a
8 b

30˚
b
60˚
Solve It a

Solve It