Question

In JKL, mJ = 90, mK = 30, and mL = 60. Which of the following statements about JKL are true?

Answer 1

The correct answers are:

KL = 2*JL; JK = (√3)JL; and JK = ((√3)/2)KL

Explanation:

This is a 30-60-90 right triangle.  This type of triangle has a special relationship among the sides.  Let the smallest side, across from the 30° angle, be t.  This means JL = t.

The hypotenuse of the triangle is two times the length of the smallest side; this means that KL = 2t, which means that KL = 2*JL.

The side of the triangle opposite the 60° angle will be the "medium sized" side; it is equal to √3 times the smallest side, or √3t; this gives us that JK = √3t = (√3)JL.

Comparing JK to KL, we have

$\frac{t\sqrt{3}}{2t}$

The t on top and bottom cancel out, leaving us with the ratio (√3)/2.  This means that JK = ((√3)/2)KL.

Answer 2

Jk=sqr3(JL)
KL-2(JL)
JK=(sqr3/2)KL