# Help Solve Lengths of Sides

## Trig Triumph Game: Level 3 Help

### Right Triangles

Find the lengths of sides of a right triangle with the calculator and the Pythagorean Theorem.
The Pythagorean Theorem is `a`

+ ^{2}`b`

= ^{2}`c`

.
Where ^{2}`c`

is the hypotenuse. `a`

, and `b`

are the other legs of a right triangle.

For example find the length of
`c`

, when given the length of `a`

and `b`

.
First, square the length of `a`

, and save the value.
Second square the length of `b`

, and save the value.
Third add `a`

and ^{2}`b`

together to
obtain ^{2}`c`

. Finally find the square root of ^{2}`c`

.
The square root of ^{2}`c`

equals your answer, the length of leg ^{2}`c`

.

Suppose you only have the lengths of the hypotenuse `c`

, and one leg of the
right triangle `a`

.
The hypotenuse is always longer than the other legs of a right triangle.
Subtract `a`

from ^{2}`c`

,
to obtain a positive number. The square root of a negative number is not a valid length.
Your answer equals the square root of (^{2}`c`

- ^{2}`a`

).
^{2}

The calculator processes values for trigonometric functions with degrees, rather than radians. The game's answers are rounded to three decimal precision. In other words, a maximum of three digits display after the decimal point.

### Post Your Score Online

Select the Post Score

button to post your score online.
See how your score compares to others in the Trig Triumph Hall of Fame.

#### Rounding Errors

Trig Triumph rounds the *final*
answer to the nearest thousandth (3 digits after the decimal point).
Often rounding each step in a series introduces `rounding errors`

.
The final result may be too high, when more than one step in the series `rounds up`

.
The final result may be too low, when more than one step in the series `rounds down`

.

Therefore don't round numbers while playing. The Trig Triumph game rounds the final result. If you don't need a calculate for the final answer, then round to the nearest thousandth. The Trig Triumph game allows for small rounding differences. However it's helpful to understand for future math projects.

### Reset Level Three

Select the Reset

button at the bottom of the page, to
begin this level again. Reset

allows you to play the
level over again and increase your score. Reset

assigns zero to
your score for this level, then displays the first question for this level.