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Popular Trigonometry >

cos(W)=(170^2+173^2-125^2)/(2(170)(173))

Solution

cos (W) = \frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 ( 170 ) ( 173 )}

Solution

W = 0.74584 \dots + 2 πn, W = 2 π - 0.74584 \dots + 2 πn

+1

Radians

W = 0.74584 \dots + 6.28318 \dots n, W = 5.53733 \dots + 6.28318 \dots n

Solution steps

cos (W) = \frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 ( 170 ) ( 173 )}

Simplify

\frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 \cdot 170 \cdot 173} : \frac{10801}{14705}

\frac{17 0 ^{2} + 17 3 ^{2} - 12 5 ^{2}}{2 \cdot 170 \cdot 173}

17 0^{2} + 17 3^{2} - 12 5^{2} = 43204

17 0^{2} + 17 3^{2} - 12 5^{2}

17 0^{2} = 28900

= 28900 + 17 3^{2} - 12 5^{2}

17 3^{2} = 29929

= 28900 + 29929 - 12 5^{2}

12 5^{2} = 15625

= 28900 + 29929 - 15625

Add/Subtract the numbers:

28900 + 29929 - 15625 = 43204

= 43204

= \frac{43204}{2 \cdot 170 \cdot 173}

Multiply the numbers:

2 \cdot 170 \cdot 173 = 58820

= \frac{43204}{58820}

Cancel the common factor:

4

= \frac{10801}{14705}

Apply trig inverse properties

cos (W) = \frac{10801}{14705}

General solutions for

cos (W) = \frac{10801}{14705}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

W = arccos (\frac{10801}{14705}) + 2 πn, W = 2 π - arccos (\frac{10801}{14705}) + 2 πn

W = arccos (\frac{10801}{14705}) + 2 πn, W = 2 π - arccos (\frac{10801}{14705}) + 2 πn

Show solutions in decimal form

W = 0.74584 \dots + 2 πn, W = 2 π - 0.74584 \dots + 2 πn

Graph

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