If a car goes around a turn too quickly, it can leave tracks that form an arc of a circle. By finding the radius of the circle,
accident investigators can estimate the speed of the car. To find the radius, accident investigators choose points A and B on the tire marks. Then, the investigators find the midpoint C of AB¯¯¯¯¯¯¯¯. Use the diagram to find the radius r of the circle. Round your answer to the nearest tenth.
2 answers:
Answer: 155.7
Detailed solution:
Start with the given information.
Length of segment AC is 130 feet.
Length of segment CD is 70 feet.
Apply the Pythagorean Theorem here, where equals
plus
.
To determine segment CE, calculate r minus 70.
Thus, equals
plus
.
Expression: equals 16,900 plus
minus 140r plus 4,900.
Move -140r to the left side, eliminate the two , then combine 16,900 and 4,900.
This results in 140r equals 21,800.
Divide both sides by 140.
The radius r calculates to 155.7 when rounded to one decimal place.
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