The distances between three cities on a map are 45 miles, 56 miles, and 72 miles. Do the positions ofthe three cities form a right triangle? How do we determine this? We use thePythagorean Theorem.
Accepted Solution
A:
Answer:The position of the three cities do not form a right-triangle. Step-by-step explanation:There are three cities on a map (say A, B, and C).
Now, the distances between them are 45 miles, 56 miles, and 72 miles.
i.e. AB= 45 miles, BC= 56 miles and CA =72 miles.
If the three cities A, B, C form a right-angled triangle on the map, then applying Pythagoras Theorem AB² +BC² =AC²
or, AC= √(AB² +BC²) must be satisfied.
Now, right-hand side of the above equation =√(45²+56²) =71.84 ≠ 72 (AC)
Hence, Right-hand side ≠ Left-hand side.
Therefore, the positions of the three cities do not form a right triangle. (Answer)