Answered

Join IDNLearn.com and become part of a knowledge-sharing community that thrives on curiosity. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.

i am not sure. but i got as far as, is this close? i am not sure.

I Am Not Sure But I Got As Far As Is This Close I Am Not Sure class=

Sagot :

Answer:

5√6 mi

Explanation:

In the given figure, triangles DAC and EBC are similar.

The ratio of corresponding sides are:

[tex]\frac{DA}{EB}=\frac{AC}{BC}=\frac{DC}{EC}[/tex]

Substitute the given values:

[tex]\begin{gathered} \frac{4\sqrt[]{138}}{\sqrt[]{138}}=\frac{BC+6\sqrt[]{3}}{BC} \\ 4=\frac{BC+6\sqrt[]{3}}{BC} \\ 4BC=BC+6\sqrt[]{3} \\ 4BC-BC=6\sqrt[]{3} \\ 3BC=6\sqrt[]{3} \\ BC=\frac{6\sqrt[]{3}}{3} \\ BC=2\sqrt[]{3} \end{gathered}[/tex]

Since we already have BC and EB, we use the Pythagoras theorem:

[tex]\begin{gathered} EC^2=EB^2+BC^2 \\ EC^2=(\sqrt[]{138})^2+(2\sqrt[]{3})^2 \\ EC^2=138+12 \\ EC^2=150 \\ EC^{}=\sqrt{150} \\ EC=5\sqrt{6}\text{ mi} \end{gathered}[/tex]

The exact length of EC is 5√6 mi.

We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.