Processing Math: Done

From Förberedande kurs i matematik 1

If we introduce the dashed triangle below, the distance as the crow flies between A and B is equal to the triangle's hypotenuse, c.

One way to determine the hypotenuse is to know the triangle's opposite and adjacent sides, since Pythagoras' theorem then gives

c2=a2+b2

In turn, we can determine the opposite and adjacent by introducing another triangle APR, where R is the point on the line PQ which the dashed triangle's side of length a cuts the line.

Because we know that AP=4 and the angle at P, simple trigonometry shows that x and y are given by

x=4sin30=421=2y=4cos30=423=23

We can now start to look for the solution. Since x and y have been calculated, we can determine a and b by considering the horizontal and vertical distances in the figure.

a=x+5=2+5=7

b=12−y=12−23 

With a and b given, Pythagoras' theorem leads to

c=a2+b2=72+12−232=49+122−21223+232=205−383110km.