Question

Use the diagram at the right. Find DC. Then find DF. Round decimals to the nearest tenth. please help and fast!!

Answer 1

• DC=83.6 units

,

• DF = 33.5 units

Step-by-step explanation:

From the diagram:

The length of each leg is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

`\begin{gathered} (FC)/(DC)=(DC)/(EC) \\ \implies(72)/(DC)=(DC)/(97) \\ DC^2=72*97 \\ DC=\sqrt[]{72*97} \\ DC=83.6\text{ units} \end{gathered}`

Similarly:

`\begin{gathered} (ED)/(FD)=(FD)/(DC) \\ (97-83.6)/(DF)=(DF)/(83.6) \\ (13.4)/(DF)=(DF)/(83.6) \\ DF^2=13.4*83.6 \\ DF=\sqrt[]{13.4*83.6} \\ DF=33.5\text{ units} \end{gathered}`