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Determine the number of possible triangles.
7. A=108, a=9, b = 7

Sagot :

Complete question is;

Find all solutions for the given triangle, if possible. If no solution exists, write no solution. Round side lengths to the nearest tenth and angle measures to the nearest degree.

a = 9, b = 7, A = 108°

Answer:

c = 3.8

C = 24°

B = 48°

Step-by-step explanation:

From law of sines, we can find B.

a/sin A = b/sin B

sin B = (bsinA)/a

sin B = (7 × sin 108)/9

sin B = 0.7397

B = sin^(-1) 0.7397

B ≈ 48°

Sum of angles in a triangle = 180°

Thus;

C = 180 - (A + B)

C = 180 - (108 + 48)

C = 24°

Again, using law of sines, we have;

a/sin A = c/sin C

c = (a•sin C)/(sin A)

c = (9 × sin 24)/(sin 108)

c = 3.849

To the nearest tenth gives;

c = 3.8

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