Question

I need help with these problems

Answer 1

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

Learn more about the sine rule visit:

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