Answer:
The shortest distance from A to C is [tex]AC=5\sqrt{13}\ units[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
The shortest distance from A to C is the hypotenuse of the right triangle AYC
Applying the Pythagoras Theorem
[tex]AC^{2}=AY^{2} +YC^{2}[/tex]
step 1
Find the length YC (hypotenuse of the right triangle YBC)
Applying the Pythagoras Theorem
[tex]YC^{2}=YB^{2} +BC^{2}[/tex]
substitute the given values
[tex]YC^{2}=6^{2} +15^{2}[/tex]
[tex]YC^{2}=261[/tex]
[tex]YC=\sqrt{261}\ units[/tex]
step 2
Find the shortest distance from A to C
[tex]AC^{2}=AY^{2} +YC^{2}[/tex]
substitute the given values
[tex]AC^{2}=8^{2} +\sqrt{261}^{2}[/tex]
[tex]AC^{2}=325[/tex]
[tex]AC=\sqrt{325}\ units[/tex]
[tex]AC=5\sqrt{13}\ units[/tex]
