Name: Introduction to 3D Geometry
Uploaded: 2019-07-19
Duration: 10 min 11 s
Description: The world we experience and see around us is a 3D world, and thus, it becomes important to develop our understanding of it. Let us look at the video to under...

Question

From the top of a vertical cliff

70 m

high, an observer notices a yacht at sea. The angle of depression to the yacht is

45 °

. The yacht sails directly away from the cliff, and after five minutes the angle of depression is

10 °

. How fast does the yacht sail in

{kmh}^{- 1}

?

Accepted Answer

Lets draw a figure representing given data.

Here, $A B =$ height of cliff

$B C =$ distance between ship and cliff

$\tan C = \frac{A B}{B C}$

$\Rightarrow \tan 45 ° = \frac{70}{B C}$

$\Rightarrow B C = \frac{70}{1} = 70$

Distance between ship and cliff $= 70 m$

Let $C D =$ distance travelled by ship in $5$ mins

$\tan D = \frac{A B}{B D}$

$\Rightarrow \tan 10 ° = \frac{70}{70 + C D}$ $[∵ B D = B C + C D]$

$\Rightarrow 70 + C D = \frac{70}{0.176}$

$\Rightarrow C D = 397.73 - 70$

$\Rightarrow C D = 327.73$

$∴$ Speed of ship $= \frac{distance}{time}$

$= \frac{327.73}{5} m / \min$

$= \frac{327 \cdot 73}{1000} \times \frac{1}{(\frac{5}{60})} km / hr$

$= \frac{327.73 \times 12}{1000} km / hr$

$= 3.93 km / hr$

$∴$ Speed at which ship sails away $3.93 km / hr$ .

From the top of a vertical cliff $70 m$ high, an observer notices a yacht at sea. The angle of depression to the yacht is $45 °$ . The yacht sails directly away from the cliff, and after five minutes the angle of depression is $10 °$ . How fast does the yacht sail in ${kmh}^{- 1}$ ?

Important Questions on Relationships in Space: Geometry and Trigonometry in 2D and 3D

Learn and Prepare for any exam you want !

From the top of a vertical cliff 70 m high, an observer notices a yacht at sea. The angle of depression to the yacht is 45°. The yacht sails directly away from the cliff, and after five minutes the angle of depression is 10°. How fast does the yacht sail in kmh-1?

Important Questions on Relationships in Space: Geometry and Trigonometry in 2D and 3D

Learn and Prepare for any exam you want !

From the top of a vertical cliff $70 m$ high, an observer notices a yacht at sea. The angle of depression to the yacht is $45 °$ . The yacht sails directly away from the cliff, and after five minutes the angle of depression is $10 °$ . How fast does the yacht sail in ${kmh}^{- 1}$ ?