#27: Three cities form a right triangle on a map. Cities B and C are the furthest apart. If cities A and B are 14 miles apart and cities A and Care 22 miles about,
how far about are cities B and C? Round the nearest tenth.

26.1miles

Step-by-step explanation:

f three cities A, B and C form a right triangle on a map, and the Cities B and C are the furthest apart, then the distance between cities B and C will be the hypotenuse of the triangle.

If cities A and B are 14 miles apart, then |AB| = 14miles

Also if cities A and C are 22 miles apart, then |AC| = 22miles.

To get |BC| which is the distance between cities B and C, we will use the Pythagoras theorem.

|BC|² = |AB|² + |AC|²

|BC|² = 14²+22²

|BC|² = 196+484

|BC|² = 680

|BC| = √680

|BC| = 26.1miles

This means that cities B and C are 26.1miles apart

m∠a is 90°

m∠b is 40°