Answer:
a = 3 inches , b = 3√3 inches .
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 .