Making the most out of our graphical telemetry computers.

Like with many complex instruments, there are multiple ways to solve certain problems and to measure the required inputs. Combining the various functions leads to a multitude of advanced uses.

## Finding Tangent

It is possible to use the shadow square to find the tangents of angles.

Finding tangent. Note that tan(35°) approx. 7/10 = 0.7 (umbra versa). Find the mark where the string crosses the shadow square and determine whether the result lies closer to the 10 or 12-divisions. Divide accordingly.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side: so called because it can be represented as a tangent to the circle (the line that touches the circle), from Latin linea tangens or touching line (tangere, to touch). Now since tangent equals opposite over adjacent, we can use the shadow square by dividing the cosine into tenths or twelfths, in order to easily calculate the tangent as

tan(θ) = sin(θ) / cos(θ)