Question

△KLM, LM=20 3 m∠L=105°, m∠M=30° Find: KL and KM

Answer 1

KO ⊥ LM. ∠L has measure 180° -105° -30° = 45°, so ΔKOL is an isosceles right triangle

KO also has measure 1 and KL has measure √(1²+1²) = √2 by the Pythagorean theorem.

ΔKMO is half of an equilateral triangle, so KM has measure 2, and MO has measure √(2²-1²) = √3 by the Pythagorean theorem.

Then the ratio of KM to LM is 2:(1+√3) and the ratio of KL to LM is √2:(1+√3).

KL = LM×(√2)/(1+√3) = (20√3)(√2)/(1 +√3)

KL = (20√6)/(√3 +1) = (20√6)(√3 -1)/(3 -1)

KL = 30√2 -10√6 ≈ 17.9315

KM = LM×2/(1+√3) = KL×√2

KM = (30√2 -10√6)√2

KM = 60 -20√3 ≈ 25.3590

KL/sin(M) = KM/sin(L) = LM/sin(K)

KL = sin(M)·LM/sin(K) = sin(30°)·20√3/sin(105°) ≈ 17.9315

KM = sin(L)·LM/sin(K) = sin(45°)·20√3/sin(105°) ≈ 25.3590

Answer 2

Answer:

It is the answer

mark as a brainlist