What is the general solution for 94.5^2=60^2+50^2+6000cos(θ) ?

The general solution for 94.5^2=60^2+50^2+6000cos(θ) is θ=1.07956…+2pin,θ=2pi-1.07956…+2pin

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94.5^2=60^2+50^2+6000cos(θ)

94. 5^{2} = 6 0^{2} + 5 0^{2} + 6000 cos (θ)

θ = 1.07956 \dots + 2 πn, θ = 2 π - 1.07956 \dots + 2 πn

Degrees

θ = 61.85475 \dots^{\circ} + 36 0^{\circ} n, θ = 298.14524 \dots^{\circ} + 36 0^{\circ} n

Solution steps

94. 5^{2} = 6 0^{2} + 5 0^{2} + 6000 cos (θ)

Switch sides

6 0^{2} + 5 0^{2} + 6000 cos (θ) = 94. 5^{2}

6 0^{2} = 3600

3600 + 5 0^{2} + 6000 cos (θ) = 94. 5^{2}

5 0^{2} = 2500

3600 + 2500 + 6000 cos (θ) = 94. 5^{2}

Add the numbers:

3600 + 2500 = 6100

6000 cos (θ) + 6100 = 94. 5^{2}

94. 5^{2} = 8930.25

6000 cos (θ) + 6100 = 8930.25

Move

6100

to the right side

6000 cos (θ) + 6100 = 8930.25

Subtract

6100

from both sides

6000 cos (θ) + 6100 - 6100 = 8930.25 - 6100

Simplify

6000 cos (θ) = 2830.25

6000 cos (θ) = 2830.25

Divide both sides by

6000

6000 cos (θ) = 2830.25

Divide both sides by

6000

\frac{6000 cos ( θ )}{6000} = \frac{2830.25}{6000}

Simplify

cos (θ) = 0.47170 \dots

cos (θ) = 0.47170 \dots

Apply trig inverse properties

cos (θ) = 0.47170 \dots

General solutions for

cos (θ) = 0.47170 \dots

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

θ = arccos (0.47170 \dots) + 2 πn, θ = 2 π - arccos (0.47170 \dots) + 2 πn

θ = arccos (0.47170 \dots) + 2 πn, θ = 2 π - arccos (0.47170 \dots) + 2 πn

Show solutions in decimal form

θ = 1.07956 \dots + 2 πn, θ = 2 π - 1.07956 \dots + 2 πn

What is the general solution for 94.5^2=60^2+50^2+6000cos(θ) ?
The general solution for 94.5^2=60^2+50^2+6000cos(θ) is θ=1.07956…+2pin,θ=2pi-1.07956…+2pin