Find the missing lengths of the sides

a = 3 inches  , b =  3√3 inches  .

Step-by-step explanation:

Given  : 90 -60 -30 triangle .

To find : Find the missing Lengths of the sides.

Solution : We have given 90 -60 -30 triangle with hypotenuses = 6 in.

By the 90 -60 -30 triangle rule  :  The hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle and the length of the longer leg is 3√ times the length of the shorter leg.

Then Shorter leg = a longer leg = b.

Hypotenuse = 2 * Shorter leg .

Plug the values.

6 =  2 *  Shorter leg .

On dividing both sides by 2

Shorter leg (a)  = 3 inches .

Then by the rule :  longer leg is 3√ times the length of the shorter leg.

Longer leg =  3√Shorter .

Longer leg (b)  =  3√3 inches  .

Therefore, a = 3 inches  , b =  3√3 inches  .