In triangle ABC, \( AC = 19 \, \text{cm} \), \( BC = 17 \, \text{cm} \), and \(\angle BAC = 60^\circ\).
Calculate the size of \(\angle ABC\).
Answer (2)
s in ∠ A BC ∣ A C ∣ = s in ∠ B A C ∣ BC ∣ ∣ A C ∣ = 19 c m ; ∣ BC ∣ = 17 c m ; ∣∠ B A C ∣ = 6 0 o ; ∣∠ A BC ∣ = x s in x 19 = s in 6 0 o 17 cross m u lt i pl y 17 s in x = 19 s in 6 0 O 17 s in x = 19 ⋅ 3 3 / : 17 s in x = 51 19 3 s in x ≈ 0.6453 ⇒ x ≈ 4 0 o 1 1 ′ A n s w er : ∣∠ A BC ∣ ≈ 4 0 o 1 1 ′
Using the Law of Sines, we calculated ∠ A BC ≈ 40. 5 ∘ in triangle ABC with given sides and angle. The ratio of sides to the sine of the opposite angles helps us find the missing angle. The final result is approximately 40 degrees and 30 minutes.
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