A person walks 25.0 degrees north of east for 3.10 km. How far would another person walk due north and due east to arrive at the same location?
I don't understand how I could calculate the needed distance accuratly. I used 3.1*sin(25) + 3.1*cos(25). But I still think I'm getting the calculations wrong. Could someone please help me?
you have it correct. Paste this in your google search window
3.1*sin(25degrees) + 3.1*cos(25degrees)
To answer this question accurately, we need to break down the given information and use some basic trigonometry.
First, let's visualize the situation. We have a person walking 25.0 degrees north of east for a distance of 3.10 km. This forms a right triangle, where the hypotenuse represents the distance the person has walked in a straight line, and the legs represent the distances the person has walked north and east.
To find the distance the second person needs to walk due north and due east, we need to find the lengths of the two legs of the triangle.
To find the length of the leg going north, we can use the sine function. The formula is:
length_north = hypotenuse * sin(angle)
In this case, the angle is 25.0 degrees, and the hypotenuse is 3.10 km. Therefore:
length_north = 3.10 km * sin(25.0°)
Calculating this, we find:
length_north ≈ 1.33 km
Next, let's find the length of the leg going east. We can use the cosine function for this. The formula is:
length_east = hypotenuse * cos(angle)
Using the same values:
length_east = 3.10 km * cos(25.0°)
Calculating this, we find:
length_east ≈ 2.80 km
So, the second person needs to walk approximately 1.33 km due north and approximately 2.80 km due east to arrive at the same location as the first person who walked 25.0 degrees north of east for 3.10 km.