30 60 90 Triangle

30-60-90 Right Triangles

Evaluating a 30-60-90 triangle

• The short leg is always between the 60 and 90. This leg is always the one we use to measure.

• The long leg is always 

   $\sqrt{3}$   times longer than the short leg

• The hypotenuse (diagonal) is always twice the short leg

When you know the shortest leg

• Multiply the short leg by  $\sqrt{3}$  to get the longer leg

• Multiply the short leg by 2 to get the hypotenuse

Multiple Choice

Find the value of x.

• 5

• 5√3

• 5√2

• 10

Multiple Choice

Find the value of y.

• 5

• 5√3

• 5√2

• 10

Multiple Choice

Find the value of x.

• 7

• 7√2

• 7√3

• 14

Multiple Choice

Find the value of x.

• 3

• 3√2

• 3√3

• 6

Multiple Choice

Find x.

• 10
• 10√2
• 5√3

When you know the length of the Hypotenuse

• Divide by 2 to get the length of the short leg

• To get the length of the longer leg when you know the hypotenuse, it is easiest to find the length of the short leg first then multiply by  $\sqrt{3}$  

Multiple Choice

Find the value of x.

• 14

• 14√2

• 14√3

• 28

Multiple Choice

Find the value of y.

• 14

• 14√2

• 14√3

• 28

Multiple Choice

Find the value of x.

• 4

• 4√2

• 4√3

• 8

Multiple Choice

Find the value of y.

• 4

• 4√2

• 4√3

• 8

Multiple Choice

Find the value of x.

• 3

• 3√2

• 3√3

• 6

Multiple Choice

Find the value of y.

• 3

• 3√2

• 3√3

• 6

When you know the length of the longer leg

• Find the length of the short leg by dividing by  $\sqrt{3}$  

• Once you know the length of the short leg, multiply by 2 to get the hypotenuse.

Multiple Choice

Find x.

• 4
• 2
• √3
• 2√2

Multiple Choice

Find x.

• 10
• √3
• 5
• 10√3