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Popular >

17.6^2=15^2+13.1^2-2(15)(13.1)*cos(A)

Solution

17. 6^{2} = 1 5^{2} + 13. 1^{2} - 2 (15) (13.1) \cdot cos (A)

Solution

A = 1.34796 \dots + 2 πn, A = 2 π - 1.34796 \dots + 2 πn

+1

Degrees

A = 77.23267 \dots^{\circ} + 36 0^{\circ} n, A = 282.76732 \dots^{\circ} + 36 0^{\circ} n

Solution steps

17. 6^{2} = 1 5^{2} + 13. 1^{2} - 2 (15) (13.1) cos (A)

Switch sides

1 5^{2} + 13. 1^{2} - 2 \cdot 15 \cdot 13.1 cos (A) = 17. 6^{2}

Multiply the numbers:

2 \cdot 15 \cdot 13.1 = 393

1 5^{2} + 13. 1^{2} - 393 cos (A) = 17. 6^{2}

1 5^{2} = 225

225 + 13. 1^{2} - 393 cos (A) = 17. 6^{2}

13. 1^{2} = 171.61

225 + 171.61 - 393 cos (A) = 17. 6^{2}

Add the numbers:

225 + 171.61 = 396.61

- 393 cos (A) + 396.61 = 17. 6^{2}

17. 6^{2} = 309.76

- 393 cos (A) + 396.61 = 309.76

Move

396.61

to the right side

- 393 cos (A) + 396.61 = 309.76

Subtract

396.61

from both sides

- 393 cos (A) + 396.61 - 396.61 = 309.76 - 396.61

Simplify

- 393 cos (A) = - 86.85

- 393 cos (A) = - 86.85

Divide both sides by

- 393

- 393 cos (A) = - 86.85

Divide both sides by

- 393

\frac{- 393 cos ( A )}{- 393} = \frac{- 86.85}{- 393}

Simplify

\frac{- 393 cos ( A )}{- 393} = \frac{- 86.85}{- 393}

Simplify

\frac{- 393 cos ( A )}{- 393} : cos (A)

\frac{- 393 cos ( A )}{- 393}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{393 cos ( A )}{393}

Divide the numbers:

\frac{393}{393} = 1

= cos (A)

Simplify

\frac{- 86.85}{- 393} : 0.22099 \dots

\frac{- 86.85}{- 393}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{86.85}{393}

Divide the numbers:

\frac{86.85}{393} = 0.22099 \dots

= 0.22099 \dots

cos (A) = 0.22099 \dots

cos (A) = 0.22099 \dots

cos (A) = 0.22099 \dots

Apply trig inverse properties

cos (A) = 0.22099 \dots

General solutions for

cos (A) = 0.22099 \dots

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

A = arccos (0.22099 \dots) + 2 πn, A = 2 π - arccos (0.22099 \dots) + 2 πn

A = arccos (0.22099 \dots) + 2 πn, A = 2 π - arccos (0.22099 \dots) + 2 πn

Show solutions in decimal form

A = 1.34796 \dots + 2 πn, A = 2 π - 1.34796 \dots + 2 πn

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