a = 12,b = 22,c = 25.96186
∠A = 27.417°,∠B = 57.583°,∠C = 95°
What is law of sine?
Law of sine states that the ratio sine of an angle and its opposite side in a triangle is same for all 3 angles and their corresponding sides.
sinA/a=sinB/b=sinC/c
What is law of cosine?
Law of cosine is the generalized Pythagoras theorem is applied. It is applied for measuring one side where the opposite angle and other two sides are given.
c²=a²+b²-2abcosC
here given,
a = 12
b = 22
∠C = 95°
Applying law of cosine,
c²=a²+b²-2abcosC
=12²+22²-2.12.22.cos95°
=674.018
⇒c=√674.018
⇒c=25.96
Applying law of sine
sinA/a=sinC/c
⇒sinA=(a/c)sinC
⇒sinA=(12/25.96)sin95°=0.46
⇒A=sin⁻¹(0.46)
⇒A=27.417°
As we know sum of the 3 angles in a triangles are 180°.
∠B=180°-(∠A+∠C)=180°-(27.417°+95°)=180°-(122.42)
⇒∠B=57.583°
Therefore a = 12,b = 22,c = 25.96186
∠A = 27.417°,∠B = 57.583°,∠C = 95°
Learn more about law of sine
here: https://brainly.com/question/27174058
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