You are camping with Joe and Karl. Since all three of you like your privacy, you don’t pitch your tents close together. Joe’s tent is 21.0 m from yours, in the direction 23.0° south of east. Karl’s tent is 32.0 m from yours, in the direction 37.0° north of east. What is the distance between Karl’s tent and Joe’s tent?

Step-by-step explanation:

According to the flaring, the triangle expressed in the figure is formed.

Now we have a vector A and vector B, whose components are Ax, Ay and Bx and By respectively.

To calculate these components you must use the following formulas:

Ax = A * cos [angle a] = 32 * cos 37 ° = 25.6

Ay = A * sin [angle a] = 32 * sin 37 ° = 19.3

Bx = B * cos [angle a] = 21 * cos 23 ° = 19.3

By = B * sin [angle b] = 21 * sin 23 ° = - 8.2

In the figure it can be seen that vector B is the result of vector A and vector C

Thus:

B = A + C

reorganizing is:

C = B - A

Now to calculate Cx and Cy, we will do it with the previously calculated components:

Cx = Bx - Ax = 19.3 - 25.6 = -6.3

Cy = By - Ay = -8.2 - 19.3 = -27.5

Now to calculate the value of vector C, we apply the following formula:

C ^ 2 = Cx ^ 2 + Cy ^ 2

Rearranging:

C = (Cx ^ 2 + Cy ^ 2) ^ (1/2)

C = [(-6.3 ^ 2) + (27.5 ^ 2)] ^ (1/2) = 28.2

Then the distance would be 28.2 meters.

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