Question

In ΔIJK, k = 59 cm, i = 80 cm and ∠J=106°. Find the length of j, to the nearest centimeter.

Answer 1

112 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.

Cosine 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^2=b^2+c^2-2bc*cos(A)`

In triangle IJK:

We can find the length of j using cosine rule:

`j^2=k^2+i^2-2ik*cos(J)\\\\substituting:\\\\j^2=59^2+80^2-2(80)(59)cos(106)\\\\j^2=3481+6400-(-2602)\\\\j^2=3481+6400+2602\\\\j^2=12483\\\\j=√(12483) \\\\j=112\ cm`