Questions: Find the length of the segment indicated. Round to the nearest tenth if necessary. Note: One segment of each triangle is a tangent line.

Solution Steps

The problem involves a right triangle formed by the radius of the circle, the tangent line, and the hypotenuse. The radius is 7.5 units, and the hypotenuse is 17 units.

Use the Pythagorean theorem \(a^2 + b^2 = c^2\) to find the length of the tangent line (denoted as \(a\)). Here, \(b\) is the radius (7.5 units), and \(c\) is the hypotenuse (17 units).

Substitute the known values into the Pythagorean theorem: \[a^2 + 7.5^2 = 17^2\] \[a^2 + 56.25 = 289\] \[a^2 = 289 - 56.25\] \[a^2 = 232.75\] \[a = \sqrt{232.75}\] \[a \approx 15.3\]

Final Answer