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A ship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. Find the distance of the end of the trip from the starting point.

Respuesta :

brandimarie36
70 km 027 degrees ->
north/south 70 * cos(27) = 62.37 (positive so it is to the north)
east/west 70 * sin(27) = 31.779 (positive so it is to the east)

180 kn 147 degrees ->
north/south 180 * cos(147) = -150.961 (negative so it is to the south)
east/west 180 * sin(147) = 98.035 (positive so it is to the east)

sum:
north/south: -88.59
east/west: 129.814

and to find the distance of this point from the starting point:
sqrt(-88.59^2 + 129.814^2)
sqrt(7848.1881 + 16851.768) = 157.16km
david8644

Answer:

So the angle would be 123,66º and the distance will be 183,23,

Step-by-step explanation:

To solve this you need to create a triangle rectangle with the values of the vector that you are given you just need to convert them to the X and Y in the graph:

x1=70*cos27=62,37

y1=70*sin27= 31,77

x2=180cos147=-150,96

y2=180sin147=98,03

So from this you just can calculate with the calculus of the hypothenuse:

[tex]c^2=a^2+b^2\\c^2=(62,37-150,96)^2+(62,37+98,03)^2\\c=\sqrt{25728,16+7848,18}\\ c=183,23[/tex]

So the answer is 183,23 km from the starting point.

To calculate the angle we use sin-1, by dividing adjacent/hyphotenuse:

-150,96/183,23=-,8238

Sin-1-,8323= 123,66

So the angle would be 123,66º and the distance will be 183,23,

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