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3 years ago

Draw a vector representing the course of a ship that goes 75 miles on a

Mathematics

1 answer:

Nat2105 [25]3 years ago

7 0

Answer:

The answer is below

Step-by-step explanation:

We have a vector with a magnitude of 75 miles and a direction of 300 °.

To draw it, the first thing is to make a Cartesian plane, the first thing is to know in which quadrant it would be, 300 ° is in the fourth quadrant (270 ° - 360 °), that is, it would be 30 ° (300 ° - 270 °) with respect to to the y axis negative.

Knowing this angle, we calculate the value of x and y, knowing that the magnitude of the vector is 75 miles, that is, this value would be the hypotenuse.

The value on the x-axis can be calculated using the sine of the angle, like this:

sin 30 ° = x / 75

x = sin 30 ° * 75

x = 37.5

Now to calculate the value on the y-axis it would be by means of Pythagoras and it would be:

y ^ 2 = 75 ^ 2 - 37.5 ^ 2

y ^ 2 = 4218.75

y = 64.95, -64.95 because it must be located in the fourth quadrant

Which means that to draw the vector that we are asked to do, we must draw a point from origin (0,0) to (37.5, -64.95).

Then I leave a sketch of what it would be:

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