Answer :
Answer:
AC = 6[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Using the tangent ratio in right triangle ABC and the exact value
• tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{6\sqrt{2} }{AC}[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross multiply )
AC = 6[tex]\sqrt{2}[/tex] × [tex]\sqrt{3}[/tex] = 6 × [tex]\sqrt{2(3)}[/tex] = 6[tex]\sqrt{6}[/tex]
Answer:
[tex]x=6\sqrt{6}[/tex]
Step-by-step explanation:
The given right triangle is a special 30-60-90 triangle as it angles measure 30°, 60° and 90°.
In a 30-60-90 right triangle, the side lengths are in the ratio 1 : √3 : 2:
- The side opposite the 30° angle is the shortest leg.
- The side opposite the 60° angle is the longest leg and is √3 times the length of the shortest leg.
- The side opposite the 90° angle is the hypotenuse and is 2 times the length of the shortest leg.
In this case, the side opposite the 30° angle measures 6√2 units.
To find the length of the longest leg AC, multiply the length of the shortest leg by √3:
[tex]AC=BC\cdot\sqrt{3}\\\\x=6\sqrt{2}\cdot \sqrt{3} \\\\x=6\sqrt{2\cdot 3} \\\\x=6\sqrt{6}[/tex]
Therefore, the length of side AC is:
[tex]\LARGE\boxed{\boxed{x=6\sqrt{6}}}[/tex]
