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.

How do you solve a^2=3^2+5^2-2(3)(5)cos85a^2=3^2+5^2-2(3)(5)cos85?