Question

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

Check all that apply.

A. KL = 2 • JL
B. JK = 2 • JL
C. JK = • KL
D. JL = • KL
E. KL = • JL
F. JK = • JL

Answer 1

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

Answer 2

The correct answers are:

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

Step-by-step 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

`(t√(3))/(2t)`

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