Question

A man in a boat rowing away from a lighthouse 150m high, takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60degree to 45degree. Find the speed of the boat.

Answer 1

Answer:

Let AB be the lighthouse and C and D be the two positions of the boat such that AB = 150 m, ∠ADB = 45° and ∠ACB = 60°. Let speed of the boat be X metre per minute. Therefore, CD = 2X m; Hence, the speed of the boat is 0.53 m/s

take care beautiful!♥

Answer 2

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✤ Required Answer:

✒ GiveN:

• Height of the lighthouse = 150 m
• Elevation changed from 60° to 45°
• Time taken = 2 minutes

✒ To FinD:

• Find the speed of the boat...?

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✤ How to solve?

Here, we can see two right angled triangle with one angle other than right angle is given. We are also given with the perpendicular (That is, Height of lighthouse). So, By using trigonometry, we can find the base distance and then subtract to find the distance travelled by the man.

☃️ So, Let's solve this question..$.$

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✤ Solution:

Let,

• Distance travelled by the boat or man from point D to Point A i.e. AD = x

Now, In ΔBAC,

➝ tan 45° = BC/AC

➝ tan 45° = BC/AD + DC

[ We know, AD = x]

➝ tan 45° = BC/x + DC

[ BC = 150 m]

➝ 1 = 150/x + DC

➝ x + DC = 150 m........(1)

Now, In ΔBDC,

➝ tan 60° = BD/DC

➝ √3 = 150/DC

➝ DC√3 = 150

➝ DC = 150/√3

[ Rationlize]

➝ DC = 150√3/3

➝ DC = 50√3 m

Putting value of DC in Eq.(1),

➝ x + 50√3 = 150 m

➝ x = 150 - 50√3 m

➝ x = 50√3(√3 - 1) m

Simplifying,

➝ x = 63.4 m (approx.)

So, Now we have,

• Distance travelled = 63.4 m
• Time taken = 2 min = 120 s

Finding speed of man,

➝ Speed = Distance/Time

➝ Speed = 63.4 m/120s

➝ Speed = 0.53 m/s (approx.)

✒ Speed of the man on boat = 0.53 m

☀️ Hence, solved !!

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