# Help Solve for One Angle

## Trig Triumph Game: Level Four Help

Win 40 points for each correct selection. This page explains how to solve for one angle of a right triangle.

#### Calculator for Degrees, Minutes, and Seconds

Questions in the Trig Triumph

game include angles with degrees, minutes and seconds.
The calculator allows you to insert degree, minute, and second
symbols. However the calculator doesn't execute statements
with degrees, minutes, or seconds. This section
teaches you how to solve for one angle, with degrees, minutes, and seconds.
Before submitting your final answer, always include the degree symbol .
If the angle breaks down to minutes and seconds
include the minute symbol
and the second symbol .

Use the calculator button to insert the degree symbol . Use the calculator button to insert the minute symbol . Use the calculator button to insert the second symbol .

#### Solve for Angles in Degrees

The sum of all three angles in a triangle equals 180^{0}
or 180 degrees. A right angle equals 90 degrees.
In a right triangle, the sum of the two remaining angles equals 90 degrees
because 180 - 90 = 90.
Each question includes a right angle, and the
value for a second angle
θ.

The formula:

180 = 90 (the right angle) + θ (The given angle) + θ.

Solve for the remaining angle θ.

For example given θ = 60.
Substitute θ for 60 in the
previous formula.

180 = 90 + 60 + θ

180 - 90 = 60 + θ

90 = 60 + θ

90 - 60 = θ

30 = θ

The remaining angle solution is 30.

#### Solve for Angles with Degrees, Minutes, and Seconds

##### Minutes

Each degree may be divided into 60 minutes. One minute equals 1/60 of a degree.
One degree equals 60 minutes.
The symbol for degree is ^{0}.
The symbol for minute is '.

##### Seconds

Each minute may be divided into 60 seconds. One second equals 1/60 of a second. One minute equals 60 seconds. The symbol for seconds is ''.

One degree equals 3600 seconds because 60 minutes times 60 seconds equals 3600.

Use a modification of the previous formula
to solve for angle θ
given θ = 60^{0}2'.

180^{0} = 90^{0} + 60^{0}2' + θ

180^{0} - 90^{0} = 60^{0}2' + θ

90^{0} - 60^{0}2' = θ.

Subtract 60^{0}2' from 90^{0}0'.

90^{0}0'

-60^{0}2'

Borrow one degree from 90^{0} to add 60 minutes.
Remember 89^{0}60' = 90^{0}0'.
Now subtract 89^{0}60' - 60^{0}2' = θ.

89^{0}60'

-60^{0} 2'

_________________________

29^{0}58'

Your solution is
29^{0}58' = θ.

Follow the same process with seconds. Borrow 60 seconds from the minutes column when necessary.

### 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 each step. Round the final answer down 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 Four

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.