30-60-90

30-60-90

February 4, 2021

Multiple Choice

When finding the diagonal of any

 $45\degree$  right triangle, you always do what?

• multiply the sides by  $\sqrt{2}$  

• divide the sides by  $\sqrt{2}$  

Multiple Choice

When finding the side of any

 $45\degree$   right triangle, you always 

• multiply the diagonal by  $\sqrt{2}$  

• divide the diagonal by  $\sqrt{2}$  

30 - 60 - 90 right triangles

These numbers refer to the angle measures of a right triangle

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

Multiple Choice

Given that 5 is the short leg, what is the length of the long leg, b?

• $5\sqrt{3}$

• $\sqrt{15}$

• $3\sqrt{5}$

• not enough information

b =  $5\sqrt{3}$  

To find the long leg: take the length of the short leg and multiply it by  $\sqrt{3}$  

Multiple Choice

Given that 5 is the short leg, what is the length of the hypotenuse, c?

• 10

•  $\sqrt{10}$ 

•  $5\sqrt{2}$ 

• not enough information

c = 10

To find the hypotenuse, take the length of the short side and double it.

Find n and m

• Since 12 is the hypotenuse, we know that 12 = 2n (because the hypotenuse is always 2 times the short leg

• Know that 12 = 2n

• divide by 2

• n = 6

•  $m=n\sqrt{3}$  

•  $m=6\sqrt{3}$  

Open Ended

Find y and x

Find x and y

•  $y=\frac{44}{2}=22$  

•  $x=y\sqrt{3}=22\sqrt{3}$