Question

Luke and Liam found an old castle on a recent hike.

15°
125
The sign said the tower was 30 meters high. Because of social distancing, Luke and Liam stood
meters apart while looking at the top of the castle tower.
Round to the nearest meter.

Answer 1

48 meters

Explanation:

First, use trigonometric ratios formula to find the distance of each of them from the tower. The difference between their distance from the tower will give you the distance they stood apart from each other.

Distance of the first person from the Tower with am angle of elevation of 25°:

Height of the tower = 30 meters (opposite side)

Distance from the tower = x (adjacent side)

`tan(25) = (opp)/(adjacent)`

`tan(25) = (30)/(x)`

Multiply both sides by x

`tan(25)*x = 30`

Divide both sides by tan(25)

`x = (30)/(tan(25))`

`x = 64 m` (nearest whole number)

Distance of the second person from the Tower with am angle of elevation of 15°:

Height of the tower = 30 meters (opposite side)

Distance from the tower = x (adjacent side)

`tan(15) = (opp)/(adjacent)`

`tan(15) = (30)/(x)`

Multiply both sides by x

`tan(15)*x = 30`

Divide both sides by tan(15)

`x = (30)/(tan(15))`

`x = 112 m` (nearest whole number)

Distance between both of them = 112 - 64 = 48 meters