How do you find the exact value of the third side given #triangle ABC#, #b=12.4, c=8.70, mangleA23#?

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Answer 1 · 2018-02-24T12:39:58

Third side #color(purple)(a = 5.55# #color(purple)(units#

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Given : #b = 12.4, c = 8.7, hatA = 23^@#

To find #color(red)(a#

Applying Law of cosines,

#a^2 = b^2 + c^2 - 2 bc sin A#

#a^2 = 12.4^2 + 8.7^2 - (2 * 12.4 * 8.7 * cos 23)#

#a^2 = 30.8419#

#a = sqrt 30.8419 = color(purple)(5.55# #color(purple)(units#