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

A ship leaves Shanghai on a bearing of

030 °

. It sails a distance of

500 km

to Jeju. At

B

, the ship changes direction to a bearing of

100 °

. It sails a distance of

320 km

to reach Nagasaki. Calculate the bearing and distance for the ship to return from Nagasaki to Shanghai.

Accepted Answer

Let us draw a figure for given data,

$A B =$ Distance between Shanghai and Jeju

$100 °$ Distance between Jeju and Nagasaki

$A C =$ Distance between Nagasaki and Sanghai

To find $A C$ and $x$

Redrawing the figure

Applying cosine rule to $B$ ,

$\Rightarrow \cos B = \frac{B C^{2} + A B^{2} - A C^{2}}{2 \cdot B C \cdot A B}$

$\Rightarrow \cos 110 ° = \frac{320^{2} + 500^{2} - A C^{2}}{2 \cdot 320 \cdot 500}$

$\Rightarrow (- 0.342) (320000) = 102400 + 250000 - A C^{2}$

$\Rightarrow A C^{2} = 352400 + 109440$

$\Rightarrow A C = 679.588 ≅ 680 k m$

$∴$ Distance for ship to return from Nagasaki to Shanghai $= 680 km$

Applying sine rule, we get $\frac{\sin B}{A C} = \frac{\sin C}{A B}$

$\Rightarrow \frac{\sin 110 °}{680} = \frac{\sin (180 ° - x)}{500}$

$\Rightarrow \sin (180 ° - x) = \frac{500}{680} (0.9396)$

$\Rightarrow \sin (180 ° - x) = 0.6908$

$\Rightarrow 180 ° - x = 43.69 ° ≅ 44 °$

$\Rightarrow x = 136 °$

$∴$ Required angle $= x + 100 ° = 236 °$

$∴$ Bearing that ship must sail to return from Nagasaki to Shanghai $= 236 °$

A ship leaves Shanghai on a bearing of $030 °$ . It sails a distance of $500 km$ to Jeju. At $B$ , the ship changes direction to a bearing of $100 °$ . It sails a distance of $320 km$ to reach Nagasaki. Calculate the bearing and distance for the ship to return from Nagasaki to Shanghai.

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

Learn and Prepare for any exam you want !

A ship leaves Shanghai on a bearing of 030°. It sails a distance of 500 km to Jeju. At B, the ship changes direction to a bearing of 100°. It sails a distance of 320 km to reach Nagasaki. Calculate the bearing and distance for the ship to return from Nagasaki to Shanghai.

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

Learn and Prepare for any exam you want !

A ship leaves Shanghai on a bearing of $030 °$ . It sails a distance of $500 km$ to Jeju. At $B$ , the ship changes direction to a bearing of $100 °$ . It sails a distance of $320 km$ to reach Nagasaki. Calculate the bearing and distance for the ship to return from Nagasaki to Shanghai.