Suppose a boat travels due north for 17 miles, then heads northeast for 8 miles. How far from the original starting position is the boat?

I know this deals with law of Cosines, but I'm very confused.

I tried the distance formula, but I got 26 which I know is wrong as it can't be more than the other two sides added together which would be 25.

Question

Suppose a boat travels due north for 17 miles, then heads northeast for 8 miles. How far from the original starting position is the boat?

I know this deals with law of Cosines, but I'm very confused.

I tried the distance formula, but I got 26 which I know is wrong as it can't be more than the other two sides added together which would be 25.

campbell_st · Answer

draw a diagram |dw:1429679021114:dw|

anonymous · Answer

Oh wow, thank you! I got uhm

campbell_st · Answer

so the distance will be the longest side of the triangle... because it is opposite the largest angle...

anonymous · Answer

Yes, I understand that. I'm a bit confused as to which formula to use to solve.

Sorry we just got into law of Cosine and I'm horrible with trig!

campbell_st · Answer

well you have the measure of 2 sides and the included angle so its

$$c^2 = a^2 + b^2 - 2ab \times \cos(C)$$

anonymous · Answer

64+289-2(8)(17)xCos(135)

Right?

anonymous · Answer

623.935891158

Right?

campbell_st · Answer

that looks good... but don't forget thats c^2

so you need to square root

anonymous · Answer

Which I got uhm

24.9787087568

campbell_st · Answer

well its a sensible answer... as its the longest side... I haven't calculated it...

anonymous · Answer

Well, can you check for me?