A lighthouse is a tall tower with light near the top. These are often built on islands, coasts or on cliffs. Lighthouses on water surface act as a navigational aid to the mariners and send warning to boats and ships for dangers. Initially wood, coal would be used as illuminators. Gradually it was replaced by candles, lanterns, electric lights. Nowadays they are run by machines and remote monitoring. Prongs Reef lighthouse of Mumbai was constructed in 1874-75. It is approximately 40 meters high and its beam can be seen at a distance of 30 kilometres. A ship and a boat are coming towards the lighthouse from opposite directions. Angles of depression of flash light from the lighthouse to the boat and the ship are 30 degree and 60 degree respectively. The ship which is nearer to the lighthouse has ______________ angle of depression

Answers 2

Answer:

The answer is

30 to 60 degree.

Answer:

(i) Which of the two, boat or the ship is nearer to the light house. Find its distance from the lighthouse?

Answer: The ship is nearer to the lighthouse as its angle of depression is greater.

In ∆ ACB, tan 60° = AB/BC

√3 = 40/BC

∴ BC = 40/√3

= 40√3/3 m

(ii) Find the time taken by the boat to reach the light house if it is moving at the rate of 20 km per hour.

Answer: In ∆ ADB, tan 30° = AB/DB

⇒1/√3 = 40/DB

∴ DB = 40√3

Time taken to cover this distance

= (60/2000 × 40√3) minutes

= 60√3/100

= 2.076 minutes

Step-by-step explanation:

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