Question

Aidan knows that the observation deck on the Vancouver Lookout is 130 m above the ground. He measures the angle between the ground and his line of sight to the observation deck as \(77^{\circ}\). How far is Aidan from the base of the Lookout to the nearest metre?

Answer 1

Since x is the side adjacent the \(77^{\circ}\) angle and we are given the length of the side opposite the angle, then we can use the tangent ratio to write

\(\tan=\frac{\text{opposite leg}}{\text{adjacent leg}}\)

\(\tan77^{\circ}=\frac{130}{x}\)

\(x=\frac{130}{\tan77^{\circ}}\)

\(x\approx30m\)