What is the general solution for 5^2=8^2-(11.85)^2-2(8)(11.85)(cos(A)) ?

The general solution for 5^2=8^2-(11.85)^2-2(8)(11.85)(cos(A)) is A=2.13521…+2pin,A=-2.13521…+2pin

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5^2=8^2-(11.85)^2-2(8)(11.85)(cos(A))

5^{2} = 8^{2} - (11.85)^{2} - 2 (8) (11.85) (cos (A))

A = 2.13521 \dots + 2 πn, A = - 2.13521 \dots + 2 πn

Degrees

A = 122.33908 \dots^{\circ} + 36 0^{\circ} n, A = - 122.33908 \dots^{\circ} + 36 0^{\circ} n

Solution steps

5^{2} = 8^{2} - (11.85)^{2} - 2 (8) (11.85) (cos (A))

Switch sides

8^{2} - 11.8 5^{2} - 2 \cdot 8 \cdot 11.85 cos (A) = 5^{2}

Multiply the numbers:

2 \cdot 8 \cdot 11.85 = 189.6

8^{2} - 11.8 5^{2} - 189.6 cos (A) = 5^{2}

8^{2} = 64

64 - 11.8 5^{2} - 189.6 cos (A) = 5^{2}

11.8 5^{2} = 140.4225

64 - 140.4225 - 189.6 cos (A) = 5^{2}

Subtract the numbers:

64 - 140.4225 = - 76.4225

- 189.6 cos (A) - 76.4225 = 5^{2}

5^{2} = 25

- 189.6 cos (A) - 76.4225 = 25

Move

76.4225

to the right side

- 189.6 cos (A) - 76.4225 = 25

Add

76.4225

to both sides

- 189.6 cos (A) - 76.4225 + 76.4225 = 25 + 76.4225

Simplify

- 189.6 cos (A) = 101.4225

- 189.6 cos (A) = 101.4225

Divide both sides by

- 189.6

- 189.6 cos (A) = 101.4225

Divide both sides by

- 189.6

\frac{- 189.6 cos ( A )}{- 189.6} = \frac{101.4225}{- 189.6}

Simplify

cos (A) = - \frac{101.4225}{189.6}

cos (A) = - \frac{101.4225}{189.6}

Apply trig inverse properties

cos (A) = - \frac{101.4225}{189.6}

General solutions for

cos (A) = - \frac{101.4225}{189.6}

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

A = arccos (- \frac{101.4225}{189.6}) + 2 πn, A = - arccos (- \frac{101.4225}{189.6}) + 2 πn

A = arccos (- \frac{101.4225}{189.6}) + 2 πn, A = - arccos (- \frac{101.4225}{189.6}) + 2 πn

Show solutions in decimal form

A = 2.13521 \dots + 2 πn, A = - 2.13521 \dots + 2 πn

2 + 2 sin (θ) = 4

- 4 sin (8 x) = 0

- sin (x) + 2 cos (x) = 0

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

(cosh (x)) = sinh (x)

What is the general solution for 5^2=8^2-(11.85)^2-2(8)(11.85)(cos(A)) ?
The general solution for 5^2=8^2-(11.85)^2-2(8)(11.85)(cos(A)) is A=2.13521…+2pin,A=-2.13521…+2pin