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# Ambiguous Case Problem (trig)?

Topic: Ambiguous case sine
June 27, 2019 / By Jami
Question: Given triangle ABC with sides of a = 6, b = 10 and measure of angle A = (in degrees, minutes, seconds) 31˚10', find the other sides (c) and other angle measures (B)(C) This IS an ambiguous case problem. 10 points for correct answer. Thanks

## Best Answers: Ambiguous Case Problem (trig)?

Ephah | 4 days ago
use sine rule 31.10 = 31.17 degrees a/sinA = b/sinB = c/sinC 6/sin(31.17) = 10/sin(B) 11.59 = 10/sinB sinB = 10/11.59 sin(B) = 0.86 B = 59.3 degrees so C = 180 - (A+B) = 180 -(31.17 + 59.3) = 89.53 now a/sinA = c/sinC 11.59 = c/sin(89.53) c = 11.59*sin(89.53) = 11.59 It is almost right angled triangle with c as hypotenuse
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Originally Answered: Ambiguous case trigonometry help?
Hi, Let x = distance from A to directly under the satellite and 50 - x = distance from B to directly under the satellite. If h is the height to the satellite, then tan 87 = h/x and tan 84.2 = h/(50 - x) x tan 87 = h and (50 - x) tan 84.2 = h Since both equal h, then: x tan 87 = (50 - x) tan 84.2 x tan 87 = 50tan 84.2 - x tan 84.2 x tan 87 + x tan 84.2 = 50tan 84.2 x(tan 87 + tan 84.2) = 50tan 84.2 50tan 84.2 -------------------------- = x tan 87 + tan 84.2 x = 17.017 miles <==ANSWER distance along the ground from A to be underneath the satellite h = x tan 87 = 324.709 miles <==ANSWER height of satellite If you wanted the diagonal distance from A to the satellite, it is 325.155 miles <==ANSWER, diagonal distance from A to satellite I hope that helps!! :-)

Cindra
a thank you to unravel those issues is by using making use of the regulation of Sines to unravel for the sine of the unknown perspective, ?, say. For any answer to be achievable, we could have sin ? ? a million, so anticipate that it is so. on account that ? and ? ? ? have the comparable sine, computing ? from sin ? will many times produce 2 strategies. If the sine is a million, i.e., ? = ?/2, there's a different answer. additionally, one answer could be impossible because it may produce a triangle the sum of whose angles exceeds ?. In the two of those 2 circumstances, the answer is unique; in any different case, it rather is the ambiguous case. So, the ambiguous case is whilst the unknown perspective (Z on your case) does have 2 achievable values. on your problem we've x / sin X = z / sin Z ?sin Z = z sin X / x = 7.5 sin fifty 8?/9.3 = 0.6839 ?Z = 40 3.15? or 136.80 5?. on account that 136.80 5? + fifty 8? > one hundred eighty?, the 2nd answer is impossible and Z = 40 3.15?. So, your answer is actual.
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Babette
try using this online calculator just plug in the values it should work. http://www.csgnetwork.com/trianglessacalc.html
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