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XAT 2018 — QA & DI Question 9

Height & DistanceEasy

A boat, stationed at the North of a lighthouse, is making an angle of 30° with the top of the lighthouse. Simultaneously, another boat, stationed at the East of the same lighthouse, is making an angle of 45° with the top of the lighthouse. What will be the shortest distance between these two boats? The height of the lighthouse is 300 feet. Assume both the boats are of negligible dimensions.

Answer & solution

  • A

    300 feet

  • B

    600√3 feet

  • C

    300√3 feet

  • 600 feet

  • E

    None of the above

Solution

Let LM be the lighthouse and B1 and B2 be the positions of the two boats.

In ∆LMB1,
Tan 30° = LM/MB1
⇒ MB1 = LM√3 = 300√3

Also, in ∆LMB2,
Tan 45° = LM/MB2
⇒ MB2 = LM = 300

In ∆MB1B2, 
(B1B2)2 = (MB1)2 + (MB2)2
⇒ (B1B2)2 = (300√3)2 + (300)2
⇒ (B1B2)2 = 3002 × [(√3)2 + (1)2]
⇒ (B1B2)2 = 3002 × 4
⇒ B1B2 = 300 × 2 = 600

Hence, option (d).

XAT 2018 QA & DI Q9: A boat, stationed at the North of a lighthouse, is making an angle of 30° with the top of the lighthouse. — Solution | TheCATExam