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Solving Oblique Triangle
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This video gives one example of finding all the sides and angles of an oblique triangle when you are given the lengths of two sides and the measure of the angle between those two sides. See below for some clarification of the common questions.
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Finding b...
2*9*10 = 180
81 + 100 = 181
cos(109°) ≈ -0.3256 use a calculator for this. If you get -0.5770, then your calculator is set to radians instead of degrees
181 - 180*(-0.3256) ≈ 181 - (-58.6023) = 181 + 58.6023 ≈ 239.60
sqrt(239.60) ≈ 15.48
Finding A...
Use b = 15.48 and use Law of Sines...
109 is the given measure of angle B
sin A = (9 * sin(109°)) / 15.48 ≈ (9 * 0.9455) / 15.48 NOTE: sin(109°) ≈ 0.9455 If you get 0.8167, then your calculator is set to radians instead of degrees
sin A ≈ 0.5497
After this, you need to use the inverse sine function on your calculator (and make sure your calculator is STILL set for degrees and not radians)...
A = sin-1(0.5497)
A ≈ 33.3478 °
__________________
Finding b...
2*9*10 = 180
81 + 100 = 181
cos(109°) ≈ -0.3256 use a calculator for this. If you get -0.5770, then your calculator is set to radians instead of degrees
181 - 180*(-0.3256) ≈ 181 - (-58.6023) = 181 + 58.6023 ≈ 239.60
sqrt(239.60) ≈ 15.48
Finding A...
Use b = 15.48 and use Law of Sines...
109 is the given measure of angle B
sin A = (9 * sin(109°)) / 15.48 ≈ (9 * 0.9455) / 15.48 NOTE: sin(109°) ≈ 0.9455 If you get 0.8167, then your calculator is set to radians instead of degrees
sin A ≈ 0.5497
After this, you need to use the inverse sine function on your calculator (and make sure your calculator is STILL set for degrees and not radians)...
A = sin-1(0.5497)
A ≈ 33.3478 °
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