Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are $30^{\circ}$ and $45^{\circ}$ . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

75 (\sqrt{3} - 1) m

75 (\sqrt{3} + 1) m

75 (2 \sqrt{3} - 1) m

75 (1 \sqrt{3} - 1) m

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given,
PA and BD [Both the lines are parallel]
Transversal line = AB
Now, from alternate angles,

∠ ABD = ∠ PAB

Here in the given figure,

∠ ABD = 30^{\circ}

C:UserssoftberryDownloadsP0041 JPEGQ.3.jpg

In the same way we suppose
PA and BD [Both the lines are parallel]
Transversal line = AC
Now again by alternate angles

∠ ACD = ∠ PAC

In the given figure,

∠ ABD = 45^{\circ}

As, the lighthouse is perpendicular to the ground. Thus,

∠ ADB = 90^{\circ}

In the right angled

∆

ACD

\tan 45^{\circ} = \frac{AD}{CD}

1 = \frac{75}{CD}

[

ta n 45^{\circ} = 1]

CD = 75 m

In the same way
Now, in the right-angled

∆ ABD

, we have

\tan 30 ° = \frac{AB}{BD}

\frac{1}{\sqrt{3}} = \frac{75}{BD}

[

\tan 30 ° = \frac{1}{\sqrt{3}}]

BD = 75 \sqrt{3} m

Now, calculation for the two ships distance,

CD = BD - BC

BC = (75 \sqrt{3} - 75) m

BC = 75 (\sqrt{3} - 1) m

So, distance between two ships =

75 (\sqrt{3} - 1) m

.
Correct option is 1.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!