Measure of ∠C = 77°
And, Sides of triangles are;
a = 0.95
b = 0.566
c = 0.99
What is Sine rule of triangle?
By the definition of sine rule,
sin A / a = sin B / b = sin C / c
Where, a, b, c are sides of a triangle.
Given that;
Measure of ∠A = 27°
Measure of ∠B = 76°
Since, Sum of all angles of triangle = 180°
Hence,
∠A + ∠B + ∠C = 180°
27° + 76° + ∠C = 180°
∠C = 180° - 103°
∠C = 77°
So, Measure of ∠C = 77°
Since, By the definition of sine rule,
sin A / a = sin B / b = sin C / c
Since, sin A = sin 27° = 0.95
sin B = sin 76° = 0.566
sin C = sin 77° = 0.99
Hence,
0.95 / a = 0.566 / b = 0.99 / c = 1 / k
Taking terms as;
0.95 / a = 1 / k
a = 0.95 k
And, 0.566 / b = 1 / k
b = 0.566 k
And, 0.99 / c = 1 / k
c = 0.99 k
Hence, Sides of triangles are;
a : b : c = 0.95 k : 0.566 k : 0.99 k
a : b : c = 0.95 : 0.566 : 0.99
Thus, Measure of ∠C = 77°
And, Sides of triangles are;
a = 0.95
b = 0.566
c = 0.99
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