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

Bergen 2021-05-14 Answered

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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Expert Answer

Adnaan Franks

Answered 2021-05-15 Author has 92 answers

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

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

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

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

$x \approx 30 m$

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