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 sig

Right triangles and trigonometry

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?

2021-05-15

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

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

$$\tan77^{\circ}=\frac{130}{x}$$

$$x=\frac{130}{\tan77^{\circ}}$$

$$x\approx30m$$