From the top of a tower the angle of depression of a boat is 60 degrees. If the tower is 50 metres high, how far is the boat from the foot of the tower (to the nearest metre).

29 m

Step-by-step explanation:

Given:

Height of tower h = 50

Angle of depression θ = 60°

The distance d between the boat and the tower is;

Applying trigonometry;

Tanθ = opposite/adjacent

θ = angle of depression

Opposite = height of tower

Adjacent = distance from the boat to the bottom of the tower.

Substituting we have;

Tan60° = h/d = 50/d

d = 50/tan60°

d = 28.86751345948

d = 29 m (to the nearest meter)

the boat is 29 meters from the foot of the tower