From the mast head of a ship the angle of depression of a boat is tan -1 5-12 If the mast head is 100 metres- The distance of the boat from the ship is

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Standard XII

Mathematics

Properties Derived from Trigonometric Identities

From the mast...

Question

From the mast head of a ship the angle of depression of a boat is ${tan}^{- 1} (\frac{5}{12})$ If the mast head is 100 metres. The distance of the boat from the ship is

120 m

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180 m

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240 m

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None of these

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Solution

The correct option is C $240 m$
$A B$ is the mast and $C$ is the boat
Using cotangent rule, we have
$\frac{A C}{A B} = cot θ = \frac{12}{5}$
$\Rightarrow A C = 100 \times \frac{12}{5} m = 240 m$
Hence, the distance of board from the ship is $240 m$ .

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From the mast head of a ship the angle of depression of a boat is tan−1(512) If the mast head is 100 metres. The distance of the boat from the ship is

The correct option is C 240mAB is the mast and C is the boatUsing cotangent rule, we haveACAB=cotθ=125⇒AC=100×125m=240mHence, the distance of board from the ship is 240m.

From the mast head of a ship the angle of depression of a boat is ${tan}^{- 1} (\frac{5}{12})$ If the mast head is 100 metres. The distance of the boat from the ship is

The correct option is C $240 m$
$A B$ is the mast and $C$ is the boat
Using cotangent rule, we have
$\frac{A C}{A B} = cot θ = \frac{12}{5}$
$\Rightarrow A C = 100 \times \frac{12}{5} m = 240 m$
Hence, the distance of board from the ship is $240 m$ .