Work out the bearings

Step-by-step explanation:

Use Pythagorean Theorem: a^2+b^2=c^2  (a squared plus b squared equals c squared), where a and b are legs from the 90 degree angle and c is the opposite side of the triangle.

So for part a: a=AB=30  b=AC=30 and c=BC

    a^2 +b^2  =  c^2  Plug in the knowns

  30^2 +30^2=c^2  Use Pemdas, Exponents first.

30^2=900  Simplify the equation

900+900=c^2      Simplify again

1800=c^2  Now to get rid of the ^2 we need to know the square root of 1800.

It is 42.426406871(There are more numbers in the decimal.  Choose your stopping point and round)  I'm going to round to the hundredths.

So, the answer to part a is 42.43 kilometers.  

Now for part b.   a=AD=45   b=AB=30  c=DB

Same equation

a^2     +  b^2    =c^2     Plug in the knowns

45^2   +  30^2  =c^2       Simplify

2025  +  900    =c^2       Simplify

2925     =c^2                      Find the square root

54.3083269  Round to the decimal place needed.  I'm going with Hundredths.

Part b answer is 54.31 kilometers.

a 270° rotation about point p says on e d g e n u it y (had to space it out because it says it's a misspelling so i couldn't submit it