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.
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