# 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 sig

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?

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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

$\mathrm{tan}=\frac{\text{opposite leg}}{\text{adjacent leg}}$

$\mathrm{tan}{77}^{\circ }=\frac{130}{x}$

$x=\frac{130}{\mathrm{tan}{77}^{\circ }}$

$x\approx 30m$