Mathematics: Application of Sine and Cosine Law (Essay Sample)

Application of Sine and Cosine Law
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Application of Sine and Cosine Law
723014202019BaC15 cm A30 CM BaC15 cm A30 CM Question 1. Solve for α in the oblique triangle ABC, and sides AB = 30, AC = 15 and angle B = 20°
305054033346200200
We can apply the laws of side and cosine to solve for side a
991235305435BaCb Ac BaCb Ac
If triangle ABC is an oblique triangle then, according to the law of sine
Sine Aa = Sine Bb = Sine Cc
For the above case, it would be
Sine∠ A(AB) = Sine∠ B(AC) = Sine∠ C(CB)
Where ∠B is 200 and side AC = 15 cm
Sine∠ Aa = Sine 2015 = Sine ∠C30
Taking
Sin 2015 = Sin ∠C30,
And using a scientific calculator to degree mode, we can find angle C
Sine 2015 = Sine C30
Sine C = 30 xSin 2015
Sine C = 30 x 0.342015
Sine C = 0.6840
C = sine-10.6840
Angle C = 43.160
Angle C = 43.160, Angle B = 200 and angle A=?
Since angles in a triangle add up to 1800
Then, ∠ A+∠ B +∠ C = 1800
43.160 + 200+∠ A = 1800
∠ A = 1800 – 43.160-200
∠ A is equal to 116.840
If angle A is 106.840, then
Sin 116.84a = Sin 2015
a= 15x Sin 116