The angles of depression of two ships from the top of a light house are 60° and 45° towards east. If the ships are 300 m apart, the height of the light house is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 150(3 + √3) meter
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Application |
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n triangle PQS: tan 60 = PQ/QS ⇒ √3 = PQ/QS PQ = √3 QS ……… (1) In triangle PQR: tan 45 = PQ/QR ⇒ 1 = PQ/QR ⇒ PQ = QR ………….. (2) ⇒ QR = √3 QS ⇒ √3 QS = QS + 300 ⇒ QS (√3 – 1) = 300 ⇒ QS = 300/(√3 – 1) × [(√3 + 1)/(√3 + 1)] ⇒ QS = 300/2 × (√3 + 1) ⇒ QS = 150 (√3 + 1) From equation 1: PQ = 150 (√3 + 1) × √3 ⇒ PQ = 150 (3 + √3) meter |
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