Answer:
565.3 cm
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.
Sine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
In triangle KLM:
∠K + ∠L + ∠M = 180° (sum of angles in a triangle)
∠K + 107 + 18 = 180
∠K + 125 = 180
∠K = 55°
We can find the length of k using sine rule:
[tex]\frac{l}{sinL}=\frac{k}{sinK} \\\\substituting:\\\\\frac{660}{sin(107)}=\frac{k}{sin(55)} \\\\k=\frac{660}{sin(107)}*sin(55)\\\\k=565.3\ cm\\[/tex]
