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Answer:
see explanation
Step-by-step explanation:
Using the Cosine rule
a² = b² + c² - 2abcosA ← Rearranging for cosA gives
cosA =
(a)
let a = 10, b = 7, c = 8 and A = α, then
cosα = =
=
, thus
α = (
) ≈ 83° ( to the nearest degree )
(b)
let the angle opposite side 7 be x
Using the Sine rule
=
( cross- multiply )
10sinx = 7sin83 ( divide both sides by 10 )
sinx = , thus
x = (
) = 44°
The third angle can be found using the sum of angles in a triangle
third angle = 180° - (83 + 44)° = 180° - 127° = 53°
The 3 angles are 83°, 44°, 53°