# Aidan knows that the observation deck on the Vancouver Lookout is 130 m above the ground. He measures the angle between the ground

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°. How far is Aidan from the base of the Lookout to the nearest metre?

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Arnold Odonnell

"Let x be the distance from the base of the plateau to you. Draw the situation as shown: [Triangle]
Since x is the side adjacent the 77° angle and we are given the length of the side opposite the angle, then we can use the tangent ratio to write: $$\displaystyle{\tan{=}}\frac{{{o}{p}p}}{{a{d}{j}}}$$

$$\displaystyle\frac{{ \tan{{77}}^{\circ}}}{{ \tan{{60}}^{\circ}}}$$

$$\displaystyle{x}=\frac{130}{ \tan{}}$$

$$x = 30\ m$$