Question

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

Answer 1

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*6=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=√(184.96) \\ x=13.6\text{ units} \end{gathered}`

Hence, the answer is 13.6 units