Question

. [15 points] Alex is at the northernmost point of a circular parking lot with radius 26 feet. Dylan stands 22.4 feet west and 27 feet south of the southernmost point of the parking lot. Dylan walks due north until he hits the edge of the parking lot. Then, he turns and walks in a straight line towards the easternmost point of the parking lot. How close does Dylan get to Alex

Answer 1

Answer:

31.925 ft

Step-by-step explanation:

A diagram is needed to visualize Dylan's movement to Alex see below

thus (-22.4)² + y²  = 26²

y² = 26² - (22.4)² = 174.24

y = -√174.2 = - 13.2 ft note due south

closest point at intersection

3/11*  ( x- 26) = -11/3 x * + 26

3/11 x - 78/11 = -11/3x + 26

3/11 x +11/3x = 26 + 78/11

130/33 x = 364/11

x = 364/11 * 33/130 = 8.4

then y = 3/11 * (x -26)

      x = 8.4 substitute, gives y = 3/11 * (8.4 -26) = -4.8

distance from (8.4 , -4.8) to (0 , 26)

√[(0 -8.4)² +  ( 26-(-4.8))² ] = √[( -8.4)² +  ( 30.8)² ] = 31.925 ft