If KL=3cm,KM=7cm and LM=5cm.Calculate the angle K,M and the area of angle KLM

Answer 1

Use Law of Cosines.

CosK = (l^2 + m^2 -k^2) / 2lm,
CosK = (&^2 + 3^2 - 5^2) / 2*7*3,
1. CosK = 20 / 42 = 0.47619,
K = 61.56 Deg.

2. sinK/k = sinM/m,
sin61.56/5 = sinM/3,
5*sinM = 3*sin61.56,
Divide both sides by 5:
sinM = 0.6*sin61.56 = 0.52759,
M = 31.84 Deg.

3. L = 180 -61.56 - 31.84 = 86.6 Deg.

4. Area = 0.5*l*m*sinK,
Area = 0.5*7*3*sin61.56 = 9.23cm^2.

Answer 2

Correction:CosK=(7^2 + 3^2 - 5^2)/2*7*3