\overline{AB} = AB_STRING
\overline{OPPOSITE_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIN , \cos( \angle ANGLE ) = COS , \tan( \angle ANGLE ) = TAN
OPPOSITE_VALUEADJACENT_VALUEAB_STRINGWRONG_AWRONG_B\overline{AB} is the hypotenuse
\overline{OPPOSITE_NAME} is opposite to \angle ANGLE
SOH CAH TOA
We know the hypotenuse and need to solve for the opposite side so we can use the sine function (SOH)
\displaystyle \sin( \angle ANGLE ) = \frac{\text{OPPOSITE_TEXT}}{\text{HYPOTENUSE_TEXT}} = \frac{\overline{OPPOSITE_NAME}}{\overline{AB}}= \frac{\overline{OPPOSITE_NAME}}{AB_STRING}
\displaystyle \overline{OPPOSITE_NAME}=AB_STRING \cdot \sin( \angle ANGLE ) = AB_STRING \cdot SIN = OPPOSITE_VALUE
\overline{OPPOSITE_NAME} = OPPOSITE_VALUE
\overline{AB} = {?}
\displaystyle \sin( \angle ANGLE ) = SIN , \cos( \angle ANGLE ) = COS , \tan( \angle ANGLE ) = TAN
AB_STRINGOPPOSITE_VALUEADJACENT_VALUEWRONG_AWRONG_B\overline{OPPOSITE_NAME} is the opposite to \angle ANGLE
\overline{AB} is the hypotenuse (note that it is opposite the right angle)
SOH CAH TOA
We know the opposite side and need to solve for the hypotenuse so we can use the sin function (SOH)
\displaystyle \sin( \angle ANGLE ) = \frac{\text{OPPOSITE_TEXT}}{\text{HYPOTENUSE_TEXT}} = \frac{\overline{OPPOSITE_NAME}}{\overline{AB}} = \frac{OPPOSITE_VALUE}{\overline{AB}}
\displaystyle \overline{AB}=\frac{OPPOSITE_VALUE}{\sin( \angle ANGLE )} = \frac{OPPOSITE_VALUE}{SIN} = AB_STRING
\overline{AB} = AB_STRING
\overline{ADJACENT_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIN , \cos( \angle ANGLE ) = COS , \tan( \angle ANGLE ) = TAN
ADJACENT_VALUEOPPOSITE_VALUEAB_STRINGWRONG_AWRONG_B\overline{AB} is the hypotenuse
\overline{ADJACENT_NAME} is adjacent to \angle ANGLE
SOH CAH TOA
We know the hypotenuse and need to solve for the adjacent side so we can use the cos function (CAH)
\displaystyle \cos( \angle ANGLE ) = \frac{\text{ADJACENT_TEXT}}{\text{HYPOTENUSE_TEXT}} = \frac{\overline{ADJACENT_NAME}}{\overline{AB}}= \frac{\overline{ADJACENT_NAME}}{AB_STRING}
\displaystyle \overline{ADJACENT_NAME}=AB_STRING \cdot \cos( \angle ANGLE ) = AB_STRING \cdot COS = ADJACENT_VALUE
\overline{ADJACENT_NAME}=ADJACENT_VALUE
\overline{AB} = {?}
\displaystyle \sin( \angle ANGLE ) = SIN , \cos( \angle ANGLE ) = COS , \tan( \angle ANGLE ) = TAN
AB_STRINGOPPOSITE_VALUEADJACENT_VALUEWRONG_AWRONG_B\overline{ADJACENT_NAME} is adjacent to \angle ANGLE
\overline{AB} is the hypotenuse (note that it is opposite the right angle)
SOH CAH TOA
We know the adjacent side and need to solve for the hypotenuse so we can use the cos function (CAH)
\displaystyle \cos( \angle ANGLE ) = \frac{\text{ADJACENT_TEXT}}{\text{HYPOTENUSE_TEXT}} = \frac{\overline{ADJACENT_NAME}}{\overline{AB}} = \frac{ADJACENT_VALUE}{\overline{AB}}
\displaystyle \overline{AB}=\frac{ADJACENT_VALUE}{\cos( \angle ANGLE )} = \frac{ADJACENT_VALUE}{COS} = AB_STRING
\overline{OPPOSITE_NAME} = OPPOSITE_VALUE
\overline{ADJACENT_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIN , \cos( \angle ANGLE ) = COS , \tan( \angle ANGLE ) = TAN
ADJACENT_VALUEAB_STRINGWRONG_AWRONG_B\overline{OPPOSITE_NAME} is the opposite to \angle ANGLE
\overline{ADJACENT_NAME} is adjacent to \angle ANGLE
SOH CAH TOA
We know the opposite side and need to solve for the adjacent side so we can use the tan function (TOA)
\displaystyle \tan( \angle ANGLE ) = \frac{\text{OPPOSITE_TEXT}}{\text{ADJACENT_TEXT}} = \frac{\overline{OPPOSITE_NAME}}{\overline{ADJACENT_NAME}}= \frac{OPPOSITE_VALUE}{\overline{ADJACENT_NAME}}
\displaystyle \overline{ADJACENT_NAME}=\frac{OPPOSITE_VALUE}{\tan( \angle ANGLE )} = \frac{OPPOSITE_VALUE}{TAN} = ADJACENT_VALUE
\overline{ADJACENT_NAME} = ADJACENT_VALUE
\overline{OPPOSITE_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIN , \cos( \angle ANGLE ) = COS , \tan( \angle ANGLE ) = TAN
OPPOSITE_VALUEAB_STRINGWRONG_AWRONG_B\overline{OPPOSITE_NAME} is the opposite to \angle ANGLE
\overline{ADJACENT_NAME} is adjacent to \angle ANGLE
SOH CAH TOA
We know the adjacent side and need to solve for the opposite side so we can use the tan function (TOA)
\displaystyle \tan( \angle ANGLE ) = \frac{\text{OPPOSITE_TEXT}}{\text{ADJACENT_TEXT}} = \frac{\overline{OPPOSITE_NAME}}{\overline{ADJACENT_NAME}}= \frac{\overline{OPPOSITE_NAME}}{ADJACENT_VALUE}
\displaystyle \overline{OPPOSITE_NAME}=ADJACENT_VALUE \cdot \tan( \angle ANGLE ) = ADJACENT_VALUE \cdot TAN = OPPOSITE_VALUE