Answer: Angle K measures 34° (approximately)
Step-by-step explanation: (Please refer to the picture attached).
The triangle has been described as having sides JKL and one of the angles identified as angle JLK measures 105 degrees. Also one of the sides labelled JK measures 4.7 while another side JL measures 2.7.
The law of sine (or sine rule) shall be applied as stipulated in the question and this is most appropriate because this rule in mathematics applies when you have a triangle with two sides and one of the angles (facing one of the two sides) given, or when you have two angles and one side facing one of the angles given.
In this question, you have been given two sides, JK and JL and you also have angle K (facing side JL) given. The Sine Rule is stated as follows
SinA/a = SinB/b = SinC/c
(Note that a/SinA = b/SinB = c/SinC is also very correct)
Substituting for the known values, our sine rule can now be re-written as
SinL/4.7 = SinK/2.7
Sin 105/4.7 = SinK/2.7
(Sin 105 * 2.7)/4.7 = SinK
(0.9659 * 2.7)/4.7 = Sin K
2.60793/4.7 = Sin K
0.5549 = Sin K
Checking the values with a calculator gives you
K = 33.70
K ≈ 34°
Therefore angle K = 34°
