The angle of depression of a boat from the top of a cliff 40m high is 60m. Calculate the distance of the boat from the foot of the cliff
Let the distance of the boat from the foot of the cliff be x.
Using trigonometry, we know that:
tan 60° = opposite / adjacent
where opposite = 40m (height of the cliff) and adjacent = x (distance of boat from foot of cliff).
tan 60° = 1.732 (rounded to 3 decimal places)
1.732 = 40 / x
x = 40 / 1.732
x ≈ 23.094
Therefore, the boat is approximately 23.094 meters away from the foot of the cliff.