2
\includegraphics[max width=\textwidth, alt={}, center]{699c5e1e-1476-42cb-b3c4-ca08c4d81cb6-04_492_422_982_246}
The diagram shows triangle \(A B C\) in which angle \(A\) is \(60 ^ { \circ }\) and the lengths of \(A B\) and \(A C\) are \(( 4 + h ) \mathrm { cm }\) and \(( 4 - h ) \mathrm { cm }\) respectively.
- Show that the length of \(B C\) is \(p \mathrm {~cm}\) where
$$p ^ { 2 } = 16 + 3 h ^ { 2 } .$$
- Hence show that, when \(h\) is small, \(p \approx 4 + \lambda h ^ { 2 } + \mu h ^ { 4 }\), where \(\lambda\) and \(\mu\) are rational numbers whose values are to be determined.