Question

find the length of the segment indicated. round to the nearest tenth if necessary.
12.1
x
15.5
a. 23.9
b. 12.1
c. 13.4
d. 19.7

Explanation:

Step1: Apply Pythagorean theorem

In the right - angled triangle formed in the circle, if the two legs of the right - triangle are \(a = 12.1\) and \(b=15.5\), and the hypotenuse is \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=x^{2}\).
So \(x=\sqrt{12.1^{2}+15.5^{2}}\).

Step2: Calculate squares

First, calculate \(12.1^{2}=12.1\times12.1 = 146.41\) and \(15.5^{2}=15.5\times15.5 = 240.25\).
Then \(12.1^{2}+15.5^{2}=146.41 + 240.25=386.66\).

Step3: Calculate square root

\(x=\sqrt{386.66}\approx19.7\).

Answer:

d. 19.7