Question

Find the indicated length. Assume lines that appear to be tangent are tangent. Round to the nearest tenth if necessary.

Answer 1

Solution:

Let the missing length (hypotenuse) be represented by x

To find the value of x, we will apply the Pythagorean theorem formula which is

$(Hypotenuse)^2=(Opposite)^2+(Adjacent)^2$

Where the radius, r of the circle is

$\begin{gathered} r=6 \\ d=2r=2\times6=12\text{ units} \end{gathered}$

Where

$\begin{gathered} Opposite=d=12\text{ units} \\ Adjacent=6.4\text{ units} \end{gathered}$

Substitute the values of the opposite and adjacent into the Pythagorean theorem above

$\begin{gathered} (x)^2=(Oppos\imaginaryI te)^2+(Adjacent)^2 \\ (x)^2=12^2+6.4^2 \\ (x)^2=144+40.96 \\ (x)^2=184.96 \\ x=\sqrt{184.96} \\ x=13.6\text{ units} \end{gathered}$

Hence, the answer is 13.6 units