Question

Find the shortest distance from A to C in the diagram below.

Answer 1

Answer:

The shortest distance from A to C is $AC=5\sqrt{13}\ units$

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

$AC^{2}=AY^{2} +YC^{2}$

step 1

Find the length YC (hypotenuse of the right triangle YBC)

Applying the Pythagoras Theorem

$YC^{2}=YB^{2} +BC^{2}$

substitute the given values

$YC^{2}=6^{2} +15^{2}$

$YC^{2}=261$

$YC=\sqrt{261}\ units$

step 2

Find the shortest distance from A to C

$AC^{2}=AY^{2} +YC^{2}$

substitute the given values

$AC^{2}=8^{2} +\sqrt{261}^{2}$

$AC^{2}=325$

$AC=\sqrt{325}\ units$

$AC=5\sqrt{13}\ units$