How do you solve #a^2=3^2+5^2-2(3)(5)cos85#?

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Answer 1 · 2018-05-01T18:41:03

#a = 31.4# units

#a^2 = 3^2 + 5^2 - (2*3*5)cos 85^@#.

it seems best to first simplify the expression on the right-hand side.

#3^2 + 5^2 = 9 + 25 = 34#

#2 * 3 * 5 = 30 rarr -(2*3*5)cos 85^@ = -30cos85^@#/

#3^2+5^2-(2*3*5)cos85^@ = 34-30cos85^@#.

hence, #a^2 = 34-30cos85^@#.

since side length cannot be negative, #a# is the positive square root of #34-30cos85^@#.

putting #sqrt(34-30cos85^@)# into a calculator gives #31.38532771756#.

this can be rounded to #3# significant figures to give #31.4#.

therefore #a = 31.4# units in length.