Answer:
PO = 7
PM = 7
MJ = 11
∠PJO = 32°
∠KJL = 64°
PL ≈ 18.385
OL = 17
∠PLO = 22°
∠NLO = 44°
∠JKL = 72°
∠MKP = 36°
∠NKP = 36°
∠PKN = 36°
KN = 10
PL ≈ 13.04
PK ≈ 12.21
JL = 28
JK = 21
LK = 27
Step-by-step explanation:
The given parameters are;
The point representing the incenter of the triangle = P
Therefore PO = PM = PN = 7
tan(32°) = PM/JM = 7/JM
∴JM = 7/(tan(32°)) ≈ 11.2
∠PJO = tan⁻¹(7/11)≈ 32.47°
∠PJO = ∠PJM = 32° similar triangles
∠KJL = ∠KJP + ∠PJO = 32 + 32 = 64°
∠KJL ≈ 64°
PL = √(7² + 17²) ≈ 18.385
OL = NL = 17 similar triangles
∠PLO = sin⁻¹(7/18.385) ≈ 22.380°
∠PLO = ∠PLN = 22°
∠NLO = ∠PNL + ∠OLP ≈ 22° + 22° ≈ 44°
∠NLO ≈ 44.380°
∠JKL = 180 - (∠KJL + ∠NLO)
∠JKL = 180° - (64° + 44°) ≈ 72°
∠JKL ≈ 72°
∠MKP = ∠NKP = 72°/2 = 36°
∠MKP = 36°
∠NKP = 36°
∠PKN = ∠JKL - ∠MKP = 72° - 36° ≈ 36°
∠PKN ≈ 36°
KN = KM = 10
MJ = OJ = 11
PL = √(7² + 11²) ≈ 13.04
PK = √(7² + 10²) ≈ 12.21
JL = JO + OL = 11 + 17 = 28
JK = JM + MK = 11 + 10 = 21
LK = LN + NK = 17 + 10 = 27
