Question

How do you solve this

Answer 1

Θ ≈ 103°

Explanation:

using the Cosine rule in Δ ABC

cosB =
`(a^2+c^2-b^2)/(2ac)`

where a is the side opposite ∠ A , b the side opposite ∠ B and c the side opposite ∠ C

here a = 42 , b = 78 and c = 57 , then

cos B =
`(42^2+57^2-78^2)/(2(42)(57))`

=
`(1764+3249-6084)/(4788)`

=
`(5013-6084)/(4788)`

=
`(-1071)/(4788)` , then

B = Θ =
`cos^(-1)` ( -
`(1071)/(4788)` ) ≈ 103° ( to the nearest degree )