In ΔJKL: m∠K = 42°, JK ≈ 10.52 units, LK ≈ 22.08 units
Given:
∠LJK = 110°
∠KLJ = 28°
Side JL = 15 units
To find: ∠JKL = m∠K
We know that the sum of all the angles of a triangle is equal to 180°
∠LJK + ∠KLJ + ∠JKL = 180°
110° + 28° + ∠JKL = 180°
∠JKL = 180° - 138°
∠JKL = 42°
To find the side we use the Sine rule:
As per Sine rule:
[tex]\frac{a}{Sin A} =\frac{b}{Sin B}=\frac{c}{Sin C}[/tex]
Where a, b and c are the side opposite to ∠A, ∠B, and ∠C respectively.
Using the Sine rule in the given triangle
[tex]\frac{a}{sin 110} =\frac{15}{sin 42}=\frac{c}{sin 28}[/tex]
Solving:
[tex]\frac{a}{sin 110} =\frac{15}{sin 42}\\\\a=\frac{15}{sin 42}(sin 100)\\a=22.08 units[/tex]
Solving:
[tex]\frac{15}{sin 42}=\frac{c}{sin 28}\\\\c=\frac{15}{sin 42}(sin 28) \\c=10.52 units[/tex]
Therefore, m∠K = 42°, JK ≈ 10.52 units LK ≈ 22.08 units
For more information:
https://brainly.com/question/22288720
