Question

If AB = 58, and BC = 46, find the length of the radius to the nearest tenth. Assume BC is tangent to Circle A.

Answer 1

Applying the Pythagorean theorem, the length of the radius is: 35.3 units.

How to Apply the Pythagorean Theorem?

According to the Pythagorean theorem, the sum of the squares of the shorter sides of a right triangle equals the square of the longest side. For example, if a and b are two smaller legs of a right triangle, and c is the longest leg (hypotenuse) of the right triangle, then the Pythagorean theorem states that:

a² + b² = c².

Given the following parameters of the right triangle:

Triangle ABC is a right triangle with angle ACB as the right angle according to the tangent theorem since segment BC is tangent to Circle A

Segment AB = 58 (hypotenuse of the right triangle)

Segment BC = 46 (small leg of the right triangle)

Radius = AC (small leg of the right triangle)

Using the Pythagorean theorem, we have:

AC = √(AB² - BC²)

AC = √(58² - 46²)

AC = 35.3 units (to the nearest tenth).

Therefore, by using the Pythagorean theorem, the length of the radius of the circle, which is segment AC, to the nearest tenth is: 35.5 units.

Learn more about the Pythagorean theorem on:

brainly.com/question/16176867

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