Question

From a cliff 60m high, angles of depression of two sail boats at the same side of the cliff were observed as 45o and 60o. Find the distance between the boats.

Answer 1

Answer:

43.92 m

Step-by-step explanation:

Define x and y:

Let x be the distance of Boat A from the cliff

Let y be the distance of Boat B from the cliff

Find the distance of boat A from the cliff:

tan θ = opp/adj

tann (60) = x/60

x = 60 tan(60)

Find the distance of boat B from the cliff:

tan θ = opp/adj

tann (45) = y/60

y = 60 tan(45)

Find the distance between the two boats:

Distance = x - y

Distance = 60 tan(60) - 60 tan(45)

Distance = 60√3 - 60

Distance = 60(√3 - 1)

Distance = 43.92 m

Answer: 43.92 m