Answer:
x = 18.0
Step-by-step explanation:
We know that a tangent and a radius create a right angle at the point of tangency, or where they meet at a point on the given circle (tangent radius theorem).
Now we can say that triangle TSP is a right triangle.
We can now use the Pythagorean theorem. \(a^{2} +b^{2} =c^{2}\)
We are looking for x, which is the hypotenuse.
\(15^{2} +10^{2} =c^{2}\)
First, we'll simplify the exponents
\(225 +100 =c^{2}\)
\(325=c^{2}\)
C represents the hypotenuse, which means that we need to square root our equation (on both sides, of course) to find the hypotenuse.
\(\sqrt{325} =c\)
\(\sqrt{325}\) ≈ 18.0
