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° :
- The length of the side opposite to 30° is a.
- The length of the side opposite to 60° is a√3.
- The length of the side opposite to 90° is 2a.
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
