Question

In ΔKLM, l = 660 cm, ∠L=107° and ∠M=18°. Find the length of k, to the nearest 10th of a centimeter.

Answer 1

565.3 cm

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:

`(a)/(sinA) =(b)/(sinB) =(c)/(sinC)`

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:

`(l)/(sinL)=(k)/(sinK) \\\\substituting:\\\\(660)/(sin(107))=(k)/(sin(55)) \\\\k=(660)/(sin(107))*sin(55)\\\\k=565.3\ cm\\`