Answer plz fast plz I need help

A ship sails 250km due North qnd then 150km on a bearing of 075°.1)How far North is the ship now? 2)How far East is the ship now

olga_2 [115]

Answer:

1) 288.8 km due North

2) 144.9 km due East

3) 323.1 km

4) 207°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Cosine rule

$c^2=a^2+b^2-2ab \cos C$

where a, b and c are the sides and C is the angle opposite side c

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Draw a diagram using the given information (see attached).

Create a right triangle (blue on attached diagram).

This right triangle can be used to calculate the additional vertical and horizontal distance the ship sailed after sailing north for 250 km.

Question 1

To find how far North the ship is now, find the measure of the short leg of the right triangle (labelled y on the attached diagram):

$\implies \sf \cos(75^{\circ})=\dfrac{y}{150}$

$\implies \sf y=150\cos(75^{\circ})$

$\implies \sf y=38.92285677$

Then add it to the first portion of the journey:

⇒ 250 + 38.92285677... = 288.8 km

Therefore, the ship is now 288.8 km due North.

Question 2

To find how far East the ship is now, find the measure of the long leg of the right triangle (labelled x on the attached diagram):

$\implies \sf \sin(75^{\circ})=\dfrac{x}{150}$

$\implies \sf x=150\sin(75^{\circ})$

$\implies \sf x=144.8888739$

Therefore, the ship is now 144.9 km due East.

Question 3

To find how far the ship is from its starting point (labelled in red as d on the attached diagram), use the cosine rule:

$\sf \implies d^2=250^2+150^2-2(250)(150) \cos (180-75)$

$\implies \sf d=\sqrt{250^2+150^2-2(250)(150) \cos (180-75)}$

$\implies \sf d=323.1275729$

Therefore, the ship is 323.1 km from its starting point.

Question 4

To find the bearing that the ship is now from its original position, find the angle labelled green on the attached diagram.

Use the answers from part 1 and 2 to find the angle that needs to be added to 180°:

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{Total\:Eastern\:distance}{Total\:Northern\:distance}\right)$

$\implies \sf Bearing=180^{\circ}+\tan^{-1}\left(\dfrac{150\sin(75^{\circ})}{250+150\cos(75^{\circ})}\right)$

$\implies \sf Bearing=180^{\circ}+26.64077...^{\circ}$

$\implies \sf Bearing=207^{\circ}$

Therefore, as bearings are usually given as a three-figure bearings, the bearing of the ship from its original position is 207°

8 0

2 years ago

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Select all the expressions which are equivalent to –3(0.15 – 0.2 + 0.25p)

Sergio [31]

Answer:

–3(0.15 – 0.2 + 0.25p) = –3(0.15) + (–3)(0.2) + (–3)(0.25p)

Because the 2nd experssion is taking -3 times each number in the ( ).

hope this helps.

Step-by-step explanation:

4 0

3 years ago

A local hamburger shop sold a combined total of 628 hamburgers and cheeseburgers on Thursday. There were 72 fewer cheeseburgers

lys-0071 [83]

Answer:

278 cheeseburgers and 350 hamburgers sold on Thursday

Step-by-step explanation:

To confirm that these combined equal 628 we can add them together using the equation 278 + 350. Once confirm that these both equal 628 when combined, we can find the difference between the 350 hamburgers and 278 cheeseburgers by subtracting one from the other using the equation, 350 - 278. When you do that, you will get a difference of 72 which means that there were 72 fewer cheeseburgers sold than hamburgers.

(sorry if this is confusing, I'm not good at explaining things)

8 0

3 years ago

Marley has marbles of the same size and shape in a bag. There are 2 green, 5

mars1129 [50]

Answer:

B.) 1/15

Step-by-step explanation:

10 total marbles
3/10 - 1/1 = 2/9
3/10 × 2/9 = 1/15

6 0

3 years ago

Question 224 7/10 as decimal

atroni [7]

Answer:

224 7/10 is a mixed fraction ..so first we convert it into an improper fraction ...

=> for that follow these steps ...

=> 224 X 10 + 7

=> 2247/10

so now to get in decimals ..we divide 2247 by 10..

=> 224.7 ...

so here we got 224 7/10 in its decimal form ...

Step-by-step explanation:

hope that helps :))

4 0

3 years ago

Read 2 more answers