Question

A ship travels 200 miles due west, then adjusts its course 30° north of west. The ship continues on this course for 30 miles. Approximately how far is the ship from where it began?

Answer 1

Answer:

The answers D on Edg

Step-by-step explanation:

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Answer 2

The distance of the ship from the beginning  is 226.48 miles far apart.

What is a triangle?

A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.

For the given situation,

The diagram below shows the travelling of ship from A to C.

Let sides a = 30 miles, c = 200 miles,

The measure of angle B is $\angle CBA = 180-30$   [∵ Supplementary angle]

⇒ $\angle CBA = 150$

Here two sides and one angle of triangle are provided.

The other side of the triangle, that is the distance traveled by the ship can be found by using the law of cosines.

The formula of law of cosines,

$b = \sqrt{a^{2}+c^{2}-2ac (cosB ) }$

On substituting the values,

⇒ $b = \sqrt{30^{2}+200^{2}-2(30)(200) (cos150 ) }$

⇒ $b = \sqrt{900+40000-12000(-0.8660 ) }$

⇒ $b = \sqrt{40900+10392 }$

⇒ $b = \sqrt{51292}$

⇒ $b=226.477$ ≈ $226.48$

Hence we can conclude that the distance of the ship from the beginning  is 226.48 miles far apart.

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