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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.

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 class=

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Answer: 155.7

Step-by-step explanation:

Use what you know.

Segment AC is 130 ft

Segment CD is 70ft

If you use the Pythagorean Theorem, in this case being [tex]r^{2}[/tex] = [tex]a^{2}[/tex] + [tex]b^{2}[/tex]

To find segment CE, you would do r-70

So, [tex]r^{2}[/tex] = [tex]130^{2}[/tex] + [tex](r-70)^{2}[/tex]

[tex]r^{2}[/tex] = 16,900 + [tex]r^{2}[/tex] -140r + 4900

Add the -140r to the left side and then get rid of the two [tex]r^{2}[/tex]. Then Add 16,900 and 4900 together

You'll end up with 140r = 21,800

Divide 140 on each side.

Your final answer will be 155.7 (rounded to the nearest tenth)

The radius of the circle is 155.7 feet.

Given that

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.

We have to determine

In the radius, accident investigators choose points A and B on the tire marks. Then, the investigators find the midpoint C of AB.

According to the question

In the given figure the measure of the segment AC is 130 feet.

And the measure of the segment CD = 70 feet

And the measure of the segment CE is (r-70).

The radius of the s choose points A and B on the tire marks are given by using the Pythagoras theorem.

Pythagoras theorem states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the square of its base and height.

Then,

[tex]\rm r^2= (130)^2+(r-70)^2\\ \\ r^2= 16900+r^2+4900-140r\\ \\140r -21,800=r^2-r^2\\ \\ 140r - 21,800=0\\ \\ 140r = 21,800\\ \\ r = \dfrac{21800}{140}\\ \\ \rm r= 155.7[/tex]

Hence, the radius of the circle is 155.7 feet.

To know more about Pythagoras theorem click the link given below.

https://brainly.com/question/16914218

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