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76 Making Things Move

cosine, and tangent (abbreviated sin, cos, and tan)? Those three trigonometric
properties help you to estimate torque when, as in Figure 4-3, the line of force isn’t at
a convenient right angle to what connects it to the axis of rotation.

A right triangle has one angle that’s 90° (indicated by the box in the corner of the
triangle in Figure 4-4), and the side opposite the 90° angle, the longest side, is called
the hypotenuse. The cool thing about right triangles is that you can figure out any
one number you want—a side length or angle—just by knowing any two other
numbers and using sine, cosine, or tangent. To remember the relationships, think
SOHCAHTOA. It’s a mneumonic device to remember these formulas:

Sin (angle) = Opposite Side / Hypotenuse
Cos (angle) = Adjacent Side / Hypotenuse

Tan (angle) = Opposite Side / Adjacent Side

Use these relationships to solve for the distance of side X in Figure 4-4. All we know is
that one angle is 45° and the hypotenuse is 2 ft. Since we want to solve for the side
that is adjacent to the angle we know, we can use the cosine, like this:

cos (45) = X / 2

Now rearrange the equation to solve for X:

X = cos (45) × 2
When you type cos 45 into your calculator, the
answer should be 0.707. Multiply that by 2 to get
the distance of side X = 1.4 ft. FIGURE 4-4 Right triangle
Now, did you realize you just solved for unknown
distance d in Figure 4-3? If you assume the arm
2
is at 45° from horizontal and 2 ft long, that’s
exactly what you’ve done. In Figure 4-2, we
already figured out that the shoulder torque when
holding the can of soup straight out was 2 ft-lbs.
Now figure out the torque when the can is held
down at this 45° angle, as in Figure 4-3. The
perpendicular distance we just solved for is 1.4 ft,
multiplied by the weight of the can (1 lb), so the