Question

kimi is playing hide-and-seek with Tommy and Manuel. Tommy is hiding 12 feet south of Kimi, and Manuel is hiding due east of Tommy. If Kimi is 20 feet from Manuel, how far apart are Tommy and Manuel?

Answer 1

Tommy and Manuel are 16 ft apart

Explanation:

The locations of all three players are shown in the image below

They form a right triangle where the hypotenuse is 20 ft, and one of the legs is 12 ft. We must find the other leg.

We must use Pythagoras's theorem. Being a and b the legs of a right triangle and c its hypotenuse, then

`c^2=a^2+b^2`

Knowing c and one of the legs, say b:

`a^2=c^2-b^2`

Using the values c=20, b=12 we find

`a^2=20^2-12^2=400-144=256`

`a=√(256)=16`

So, Tommy and Manuel are 16 ft apart