Question

Mary wants to know the length of a tunnel built through a mountain. To do so, she makes the measurements shown in the figure below. Use these measurements to find the length of the tunnel.

Answer 1

Using cosine rule to solve for the length of the tunnel:

`a^2=b^2+c^2-2bccosA`

c=length of side c

a=length of side a

b=length of side b

A=angle opposite c

`\begin{gathered} a^2=116^2+247^2-2(116)(247)cos78^0 \\ a^=√(116^2+247^2-57304cos78) \\ a=250.1016 \end{gathered}`

Therefore the length of the tunnel = 250.1m