30-60-90 Triangle

30-60-90 Triangle

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30-60-90 Triangle

The 30-60-90 triangle is a special right triangle where the acute angles are always 30 and 60 degrees.

Opposite Side

Remember you have to go directly across the triangle to identify the opposite side.

Multiple Choice

What is the length of the side opposite the 30 degree angle?

• 6

• 10.392

• 12

Hypotenuse

Remember the hypotenuse is always opposite the right angle and it's the LONGEST side.

Multiple Choice

What is the length of the hypotenuse?

• 6

• 10.392

• 12

Fill in the Blank

What is the value of the opposite side (6) divided by the hypotenuse (12)?

Multiple Choice

What is the length of the side opposite the 30 degree angle?

• 2

• 3.464

• 4

Multiple Choice

What is the length of the hypotenuse?

• 2

• 4

• 3.64

Fill in the Blank

What is the value of the opposite side (2) divided by the hypotenuse (4)?

Multiple Choice

What is the length of the side opposite the 30 degree angle?

• 8.5

• 17

• 14.722

Multiple Choice

What is the length of the hypotenuse?

• 8.5

• 14.722

• 17

Fill in the Blank

What is the value of the opposite side (8.5) divided by the hypotenuse (17)?

Opposite/Hypotenuse

In a 30-60-90 triangle, the side opposite the 30 degree angle divided by the hypotenuse will always be .5!

Adjacent Leg

Leg of the triangle that is next to the focus angle.

Multiple Choice

What is the length of the side adjacent the 30 degree angle?

• 6

• 10.392

• 12

Fill in the Blank

What is the value of the adjacent side (10.392) divided by the hypotenuse (12)? (write three decimals)

Multiple Choice

What is the length of the side adjacent to the 30 degree angle?

• 2

• 3.464

• 4

Fill in the Blank

What is the value of the adjacent side divided by the hypotenuse? (Three decimals!)

Multiple Choice

What will the value of adjacent side/hypotenuse be for this triangle?

• .5

• 2

• .866

• 1.732

Conclusion

For a 30 degree angle, the opposite side/hypotenuse will always produce the ratio .5 and the adjacent leg/hypotenuse will always produce the ratio .866.