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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]

semsee45

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]

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