How do you determine the number of possible solutions, if any, using the rule for law of sines(ambiguous case) given A=35*, b=12, a=9.1?

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How do you determine the number of possible solutions, if any, using the rule for law of sines(ambiguous case) given A=35*, b=12, a=9.1?

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Answer 1 · 2015-08-05T19:34:41

See explanation.

Explanation:

Find $sin B$ $sinB$

$sin B = \frac{12 sin (35^{\circ})}{9.1} \approx 0.756365$ $sinB = (12sin(35^@))/9.1~~ 0.756365$

OK, that is less that or equal to $1$ $1$ , so there is a solution.

${sin}^{- 1} (0.756365) \approx {49.14}^{\circ}$ $sin^-1(0.756365) ~~ 49.14^@$

So $B = {49.14}^{\circ}$ $B = 49.14^@$ is one solution.
(And $C = 180 - {(35 + 49.14)}^{\circ} = {95.86}^{\circ}$ $C = 180 -(35+49.14)^@ = 95.86^@$ )

Another angle with the same sine is $180^{\circ} - {49.14}^{\circ} = {130.86}^{\circ}$ $180^@ - 49.14^@ = 130.86^@$

Add the $35^{\circ}$ $35^@$ angle we started with, to get: $165.86$ $165.86$ .
We have not gone over the $180^{\circ}$ $180^@$ total for the angles of a triangle, so $B = {130.86}^{\circ}$ $B = 130.86^@$ will give us a second solution.
(And $C = 180 - {(35 + 130.86)}^{\circ} = {14.14}^{\circ}$ $C = 180 -(35+130.86)^@ = 14.14^@$ )

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How do you determine the number of possible solutions, if any, using the rule for law of sines(ambiguous case) given A=35*, b=12, a=9.1?

1 Answer

Explanation:

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