\overline{AB}
= AB
\overline{OPPOSITE_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN , \cos( \angle ANGLE ) = SIMPLE_COS , \tan( \angle ANGLE ) = SIMPLE_TAN
OPPOSITE_VALUE
\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}
Since we have already been given \sin( \angle ANGLE )
, we can set up a proportion to find \overline{OPPOSITE_NAME}
.
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN = \frac{\overline{OPPOSITE_NAME}}{AB}
Simplify.
\overline{OPPOSITE_NAME} = OPPOSITE_VALUE
\overline{OPPOSITE_NAME} = OPPOSITE_VALUE
\overline{AB} = {?}
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN , \cos( \angle ANGLE ) = SIMPLE_COS , \tan( \angle ANGLE ) = SIMPLE_TAN
\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}}
Since we have already been given \sin( \angle ANGLE )
, we can set up a proportion to find \overline{AB}
.
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN = \frac{OPPOSITE_VALUE}{\overline{AB}}
Simplify.
\overline{AB} = AB
\overline{AB} = AB
\overline{ADJACENT_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN , \cos( \angle ANGLE ) = SIMPLE_COS , \tan( \angle ANGLE ) = SIMPLE_TAN
\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}
Since we have already been given \cos( \angle ANGLE )
, we can set up a proportion to find \overline{ADJACENT_NAME}
.
\displaystyle \cos( \angle ANGLE ) = SIMPLE_COS = \frac{\overline{ADJACENT_NAME}}{AB}
Simplify.
\overline{ADJACENT_NAME} = ADJACENT_VALUE
\overline{ADJACENT_NAME}=ADJACENT_VALUE
\overline{AB} = {?}
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN , \cos( \angle ANGLE ) = SIMPLE_COS , \tan( \angle ANGLE ) = SIMPLE_TAN
\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}}
Since we have already been given \cos( \angle ANGLE )
, we can set up a proportion to find \overline{AB}
.
\displaystyle \cos( \angle ANGLE ) = SIMPLE_COS = \frac{ADJACENT_VALUE}{\overline{AB}}
Simplify.
\overline{AB} = AB
\overline{OPPOSITE_NAME} = OPPOSITE_VALUE
\overline{ADJACENT_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN , \cos( \angle ANGLE ) = SIMPLE_COS , \tan( \angle ANGLE ) = SIMPLE_TAN
\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}}
Since we have already been given \tan( \angle ANGLE )
, we can set up a proportion to find \overline{ADJACENT_NAME}
.
\displaystyle \tan( \angle ANGLE ) = SIMPLE_TAN = \frac{OPPOSITE_VALUE}{\overline{ADJACENT_NAME}}
Simplify.
\overline{ADJACENT_NAME} = ADJACENT_VALUE
\overline{ADJACENT_NAME} = ADJACENT_VALUE
\overline{OPPOSITE_NAME} = {?}
\displaystyle \sin( \angle ANGLE ) = SIMPLE_SIN , \cos( \angle ANGLE ) = SIMPLE_COS , \tan( \angle ANGLE ) = SIMPLE_TAN
\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}
Since we have already been given \tan( \angle ANGLE )
, we can set up a proportion to find \overline{OPPOSITE_NAME}
.
\displaystyle \tan( \angle ANGLE ) = SIMPLE_TAN = \frac{\overline{OPPOSITE_NAME}}{ADJACENT_VALUE}
Simplify.
\overline{OPPOSITE_NAME} = OPPOSITE_VALUE