Question

I understand how to use and apply the cosine rule but I don't know how to do it without any angles

Answer 1

largest angle ≈ 109.6°

Explanation:

the largest angle in the triangle is the angle opposite the longest side.

Here that is the angle opposite side of 7.8 cm

let a = 7.8, b = 5.4 , c = 4.1 and A the largest angle , then

cosA =
`(b^2+c^2-a^2)/(2bc)`

=
`(5.4^2+4.1^2-7.8^2)/(2(5.4)(4.1))`

=
`(29.16+16.81-60.84)/(44.28)`

=
`(45.97-60.84)/(44.28)`

=
`(-14.87)/(44.28)`

then

A =
`cos^(-1)` (
`(-14.87)/(44.28)` ) ≈ 109.6° ( to 1 decimal place )