+244 You walk 30 m due north and then turn and walk 40 m due east. (a) draw a picture, (b) Calculate the distance you are from the starting point and the angle that you make relative to east (worth 1 point)
Think of this as a triangle: One side is 30, the other is 40, and you are trying to find the hypotenuse (I'm calling it h). Since the angle between north and east is 90 degrees, then this is a right triangle. Now, you have a side, an angle, and a side, in that order. In order to find h, you use the pythagorean theorem (since this is a right triangle), a^2+b^2=c^2, with a=30 and b=40, and so you get h=50.
By the angle "relative to east," I am a little confused about what you mean, so I will show you how to find each of the angles, and you can ignore the information to find the other two. First, The angle between the 30 m and the 40 m is 90 degrees, as I have already shown in the previous paragraph. The other two angles are a little trickier to find - you need to use trigonometry (sine = opposite over h, cosine = adjacent over h, and tangent = opposite over adjacent). You can use the inverses of these (you find them on scientific calculators like this one with the "2nd" button) to find the angles. So, for the angle between 30 m and 50 m, you can use cosine^-1: 30/50 (note that the negative one is not a type of squaring - it is saying that this is the inverse, and cosine will look like cos, since cos is cosine shorthand). This will allow you to get that this angle is 53.13 degrees. It isn't pretty, but this is the angle. Then for the third angle, since the triangle angle sum is 180 degrees and the other two angles sum to 143.13 degrees, you use subtraction to get that the last angle is 36.87 degrees.
I hope this helped!
