Question

Angle f and g are complementary and tan g=5. What is tan f?

Answer 1

If angles \( f \) and \( g \) are complementary, it means that:

\[
f + g = 90^\circ
\]

This implies that:

\[
f = 90^\circ - g
\]

The tangent of \( f \) can be expressed in terms of the tangent of \( g \) using the complementary angle identity:

\[
\tan(f) = \tan(90^\circ - g) = \cot(g)
\]

The cotangent is the reciprocal of the tangent. Given that \( \tan(g) = 5 \), we can find \( \cot(g) \):

\[
\cot(g) = \frac{1}{\tan(g)} = \frac{1}{5}
\]

Thus, we have:

\[
\tan(f) = \cot(g) = \frac{1}{5}
\]

Therefore, the value of \( \tan(f) \) is:

\[
\boxed{\frac{1}{5}}
\]