Answered

Find solutions to your problems with the expert advice available on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

In the right triangle shown! ZA = 30° and BC = 6√2.
How long is AC?
A
30°
H
C
6√2
B

In The Right Triangle Shown ZA 30 And BC 62How Long Is ACA30HC62B class=

Sagot :

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]

Semsee45idn

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]

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.