Question

A Siamese cat named Sam is 6 m from a catnip plant. The Siamese cat is 5 m from a Himalayan cat named Han. The sightlines from Sam to Han and from Sam to the plant form an angle of 108. How far is Han from the catnip plant?

Answer 1

The given information can be represented by the diagram below

From the given, and the nature of triangle given, we will use cosine formula

This is

$\begin{gathered} h^2=6^2+5^2-2\times6\times5cos108^0 \\ h^2=36+25-60(-cos(180-108)^0) \\ h^2=61-60(-cos72^0) \end{gathered}$$\begin{gathered} h^2=61+60\times0.3090 \\ h^2=61+18.541 \\ h^2=79.541 \\ h=\sqrt{79.541} \\ h=8.919m \\ h\approx8.9m \end{gathered}$