Question

In triangle ABC, AB = 5, BC = 6, and AC= 7 , the the nearest degree, what is the measurment of angle ABC

how can i find it

Answer 1

∠ ABC ≈ 78°

Explanation:

using the Cosine rule in Δ ABC

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

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

here a = BC = 6 , b = AC = 7 and c = AB = 5 , then

cos ABC =
`(6^2+5^2-7^2)/(2(6)(5))` =
`(36+25-49)/(60)` =
`(12)/(60)` , then

∠ ABC =
`cos^(-1)` (
`(12)/(60)` ) ≈ 78° ( to the nearest degree )