Question

The longer leg of a 30°-60°-90° triangle measures $9\sqrt{3}$ inches. What is the length of the shorter leg?

A. 18 inches

B. $18\sqrt{3}$ inches

C. $9\sqrt{3}$ inches

D. 9 inches

Answer 1

Answer:

D. 9

Step-by-step explanation:

The Pythagorean triple for a 30-60-90 right triangle is (x, x√3, 2x).  The side across from the 30° angle is x, the side across from the 60° angle is x√3, and the side across from the right angle is 2x (which is also the hypotenuse).  If the side across from the 60° angle is given as 9√3, we can set that equal to the identity for that leg:

9√3 = x√3 and solve for x.  Divide both sides by the √3 to get that x = 9

Answer 2

Answer:

The correct answer is option D. 9

Step-by-step explanation:

Points to remember

It a right triangle with angles 30°, 60 and 90° the n the sides are in the ratio,

Shorter leg : longer leg : hypotenuse = 1 : √3 : 2

To find the length of shorter leg

Here it is given that, longer length = 9√3

We have,

Shorter leg : longer leg : hypotenuse = 1 : √3 : 2 =  Shorter leg : 9√3: hypotenuse

Therefore shorter leg = 9√3/√3 = 9