Question

Andy calculates the distance between two locations, B and C, by measuring the angle at which the sun’s rays, AB and AC, strike the locations, as shown below.
What is the distance between the locations B and C?

33.1 km
58.6 km
80.0 km
92.4 km

Answer 1

58.6km

Answer 2

\[\Large \begin{array}{l}
\tan \theta = \frac{o}{a}\\
a = \frac{o}{{\tan \theta }}\\
BD = \frac{{80}}{{\tan 30}} = 138.564\\
CD = \frac{{80}}{{\tan 45}} = 80\\
BC = BD - CD = 58.564
\end{array}\]