Answer to Question #282372 in Geometry for lol

Question

While standing in line for the water fountain, Billy sees his lab partner 3 feet ahead of him and his best friend 9 feet to his right. Billy wants to go ask his lab partner a question, then go chat with his friend, and finally return to the water fountain line. How far will Billy have to walk in all? If necessary, round to the nearest tenth.

Answer 1

Solution:

Let B be the position of Billy, L be his lab partner's and F be his friend's.

This forms a right-angled triangle.

Apply pythagoras theorem in it.

$BL^2+BF^2=LF^2 \\ \Rightarrow 3^2+9^2=LF^2 \\\Rightarrow 9+81=LF^2 \\ \Rightarrow LF^2=90 \\ \Rightarrow LF=\sqrt{90}\approx9.5\ ft$

Total distance billy has to cover $=BL+BF+LF=3+9+9.5=21.5\ ft$