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Heights & Distances

The angles of...

Question

The angles of depression of two boats as observed from the mast head of a ship $50$ metres high are $45^{o}$ and $30^{o}$ . The distance between the boats, if they are on the same side of mast head in line with it, is

50 \sqrt{3}

metres

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0 (\sqrt{3} + 1)

metres

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50 (\sqrt{3} - 1)

metres

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50 (1 - \sqrt{3})

metres

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Solution

The correct option is C $50 (\sqrt{3} - 1)$ metres

From $△ A D C, \frac{50}{x} = T a n 45^{0} \Rightarrow x = 50 m$
From $△ A B D, \frac{50}{h + 50} = T a n 30^{0}$
$\Rightarrow h = 50 (\sqrt{3} - 1) m$

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The angles of depression of two boats as observed from the mast head of a ship 50 metres high are 45o and 30o. The distance between the boats, if they are on the same side of mast head in line with it, is

The correct option is C 50(√3−1) metresFrom △ADC,50x=Tan450⇒x=50mFrom △ABD,50h+50=Tan300⇒h=50(√3−1)m

The angles of depression of two boats as observed from the mast head of a ship $50$ metres high are $45^{o}$ and $30^{o}$ . The distance between the boats, if they are on the same side of mast head in line with it, is

The correct option is C $50 (\sqrt{3} - 1)$ metres

From $△ A D C, \frac{50}{x} = T a n 45^{0} \Rightarrow x = 50 m$
From $△ A B D, \frac{50}{h + 50} = T a n 30^{0}$
$\Rightarrow h = 50 (\sqrt{3} - 1) m$