Question

two ships sailing in the sea on the other side of the Lighthouse the angle of elevation of the top of the Lighthouse scene from the shape are 30° and 45° respectively if the height of Lighthouse is 200 m find the distance between the ship

Answer 1

Since the ships are on other side of the lighthouse, first we calculate the distance between lighthouse and both ships(let's assume D1 and D2) and then add it to get the answer.

So, for ship1, tan30°= height of the lighthouse/D1

Hence, D1= 200/(1/✓3)= 200✓3m

And for the ship2, tan45°= height of the lighthouse/D2

Hence, D2= 200/tan45°= 200m.

So the distance between the ships = (200+200✓3)m= 200(✓3+1) m

Answer 2

Define x1 and x2:

Let the distance be x1 and x2

Find the distance with 30º elevation:

tanø = adj/opp

tan(30) = 200/x1

x1 = 200/tan(30)

x1 = 200/√3

Find the distance with 45º elevation:

tanø = adj/opp

tan(45) = 200/x2

x2 = 200/tan(45)

x2 = 200

Find the total distance:

Total distance = 200/√3 + 200 = 315.46 m

Answer: The distance is 315.46 m