You are standing at point C, 45 feet from the Point State Park fountain in Pittsburgh, PA. The distance from you to a point of t

Question

3 years ago

9

angency on the fountain is
105 feet. Find the length of AC, the distance between you and your friend at point A.

1 answer:

bearhunter [10] · Answer 1 · 2022-11-05T08:03:10+03:00

The tangent line DC is perpendicular to the radius of the park

The length of AC is 245 feet

<h3>How to determine the distance AC?</h3>

To calculate the distance AC, we start by calculating the length of AB using:

DC^2 = (BC + AB) * BC

So, we have:

105^2 = (45 + AB) * 45

Evaluate the exponent

11025 = (45 + AB) * 45

Divide both sides by 45

245 = 45 + AB

Rewrite as:

AB + 45 = 245

From the figure, we have:

AC = AB + 45

Substitute AB + 45 = 245

AC = 245

Hence, the length of AC is 245 feet

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