Lesson 13.3 Checkpoint 1. Use trigonometric ratios to find the unknown side lengths of each triangle.
I really need the help I’m almost finished with my work

a. LK = 4√3, JL= 4√6

b.  PQ = 10√3, RP = 5√3

Step-by-step explanation:

a. LK =4√3,

LK=KJ= 4√3

sin(45°) = opposite/hypotenuse

hypotenuse (JL)= opposite/sin 45° = 4√3/√2/2 = 8√3/√2 = 8√3√2/2 = 4√6

b.

cos 30° = adjacent/hypotenuse = QR/PQ = 15/PQ

cos 30° = 15/PQ

PQ = 15/cos 30° = 15/√3/2)= 30/√3 = 30√3/3 = 10√3

tan 30° = opposite/adjacent = RP/QR

√3/3 = RP/QR

√3/3 = RP/15

RP = √3*15/3 = 5√3

answer: the answer for that is 22/3