Math Problem Statement

A small radio transmitter broadcasts in a 45 mile radius. If you drive along a straight line from a city 55 miles south of the transmitter to a second city 53 miles west of the transmitter, for what length of the drive will you pick up a signal from the transmitter? Round your answer to the nearest tenth of a mile.

Solution

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Circles
Distance Formula
Quadratic Equations

Formulas

x^2 + y^2 = r^2
Point-slope form of a line: y - y1 = m(x - x1)
Quadratic formula: ax^2 + bx + c = 0

Theorems

Power of a Point Theorem

Suitable Grade Level

Grades 10-12