30 60 90 triangles (quick answers please)

1) EF = 2 and DF = 4

2) KL = 4√3 and JL = 8

3) ST = 6 and RS = 6√3

4) PQ = 4.5√3 and RQ = 4.5

Step-by-step explanation:

Rules for special triangles 30°,60°,90° :

1) DE = 2√3 is opposite to 60°

⇒ 2√3 = a√3

⇒ a = 2

EF = a which is opposite to 30°.

⇒ EF = 2

DF = 2a which is opposite to 90°.

⇒ DF = 4

2) KJ = 4 is opposite to 30°

⇒ a = 4

KL = a√3 which is opposite to 60°.

⇒ KL = 4√3

JL = 2a which is opposite to 90°.

⇒ JL = 8

3) RT = 12 is opposite to 90°

⇒ 2a = 12

⇒ a = 6

ST = a which is opposite to 30°.

⇒ ST = 6

RS = a√3 which is opposite to 60°.

⇒ RS = 6√3

4) PR = 9 is opposite to 90°

⇒ 2a = 9

⇒ a = 4.5

PQ = a√3 which is opposite to 60°.

⇒ PQ = 4.5√3

RQ = a which is opposite to 30°.

⇒ RQ = 4.5

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.