Final answer:
To determine the distance between the cell phone user and tower B, use the Pythagorean theorem with the distances from the user to tower A (5.9 miles) and between towers A and B (3.2 miles), resulting in approximately 6.7 miles.
Step-by-step explanation:
The question asks for the distance between the cell phone user and tower B, given that the user is 5.9 miles from tower A, and the towers A and B are 3.2 miles apart. Since we are given that x = 84.3 and this does not relate to the information needed to solve the problem, we can ignore it. We can use the Pythagorean theorem to find the distance from the user to tower B because we are dealing with a right triangle where tower A and tower B are at two vertices, and the cell phone user is at the third vertex.
To apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (a² + b² = c²), we have:
- a = distance from tower A to the user = 5.9 miles
- b = distance between towers A and B = 3.2 miles
- c = distance from tower B to the user (which we need to find)
Plugging the values into the theorem:
5.9² + 3.2² = c²
34.81 + 10.24 = c²
45.05 = c²
c = √45.05
c ≈ 6.7 miles
The distance from tower B to the cell phone user is approximately 6.7 miles.