new − original
% Change =
100 %
(1-2)
original
While it’s certainly okay to memorize this by accident because of familiarity with it, you
should concentrate on being able to derive it using common sense (rather than working at
memorizing it).
Substituting the given values for the case at hand we obtain
m
m
3 52
.
− 3 40
.
%
s
s
Change =
%
100
m
3 40
.
s
% Change = 3. %
5
Problems Involving Right Triangles
Example 1-1: The length of the shorter side of a right triangle is x and the length of the
hypotenuse is r. Find the length of the longer side and find both of the angles, aside
from the right angle, in the triangle.
Solution:
ϕ
r
Draw the triangle such that it is obvious
x
which side is the shorter side
θ
y
Pythagorean Theorem
2
2
2
r = x + y
Subtract 2
x from both sides of the equation
2
2
−
=
2
r
x
y
Swap sides
2
2
2
y = r − x
Take the square root of both
2
sides of the equation
2
y = r − x
By definition, the sine of θ is the side
x
sinθ =
opposite θ divided by the hypotenuse
r
Take the arcsine of both sides of the
1 x
θ
sin −
=
equation in order to get θ by itself
r
By definition, the cosine of ϕ is the side
x
cosϕ =
adjacent to ϕ divided by the hypotenuse
r
Take the arccosine of both sides of the
1 x
ϕ
cos−
=
equation in order to get ϕ by itself
r
4