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Question

From the top of a lighthouse, the angle of depression to the top and bottom of a tower is 30° and 45°, respectively. If the lighthouse is 210 metres high, then find the height of the tower.

A 70(√3 – 1) metres Correct Answer Incorrect Answer
B 140√3(√3 – 1) metres Correct Answer Incorrect Answer
C 70√3(√3 – 1) metres Correct Answer Incorrect Answer
D 140(√3 – 1) metres Correct Answer Incorrect Answer

Solution

Let AB and CD be the heights of the light house and the tower, respectively So, AB = 210 metres, ∠ ADE = 30° and ∠ ACB = 45° Now, in right angled triangle ABC tan45° = AB/BC So, AB/BC = 1 Or, AB = BC So, BC = 210 metres And, BC = DE = 210 metres So, in right angled triangle AED, tan30° = AE/DE Or, AE = 210 × (1/√3) Or, AE = 70√3 Also, CD = BE So, height of tower CD = AB – AE = 210 – 70√3 = 70√3(√3 – 1) metres

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