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Popular Trigonometry >

1.65^2=0.65^2+1.77^2-2(0.65)(1.77)cos(A)

Solution

1.6 5^{2} = 0.6 5^{2} + 1.7 7^{2} - 2 (0.65) (1.77) cos (A)

Solution

A = 1.20041 \dots + 2 πn, A = 2 π - 1.20041 \dots + 2 πn

+1

Degrees

A = 68.77858 \dots^{\circ} + 36 0^{\circ} n, A = 291.22141 \dots^{\circ} + 36 0^{\circ} n

Solution steps

1.6 5^{2} = 0.6 5^{2} + 1.7 7^{2} - 2 (0.65) (1.77) cos (A)

Switch sides

0.6 5^{2} + 1.7 7^{2} - 2 \cdot 0.65 \cdot 1.77 cos (A) = 1.6 5^{2}

Multiply the numbers:

2 \cdot 0.65 \cdot 1.77 = 2.301

0.6 5^{2} + 1.7 7^{2} - 2.301 cos (A) = 1.6 5^{2}

0.6 5^{2} = 0.4225

0.4225 + 1.7 7^{2} - 2.301 cos (A) = 1.6 5^{2}

1.7 7^{2} = 3.1329

0.4225 + 3.1329 - 2.301 cos (A) = 1.6 5^{2}

Add the numbers:

0.4225 + 3.1329 = 3.5554

- 2.301 cos (A) + 3.5554 = 1.6 5^{2}

1.6 5^{2} = 2.7225

- 2.301 cos (A) + 3.5554 = 2.7225

Move

3.5554

to the right side

- 2.301 cos (A) + 3.5554 = 2.7225

Subtract

3.5554

from both sides

- 2.301 cos (A) + 3.5554 - 3.5554 = 2.7225 - 3.5554

Simplify

- 2.301 cos (A) = - 0.8329

- 2.301 cos (A) = - 0.8329

Divide both sides by

- 2.301

- 2.301 cos (A) = - 0.8329

Divide both sides by

- 2.301

\frac{- 2.301 cos ( A )}{- 2.301} = \frac{- 0.8329}{- 2.301}

Simplify

cos (A) = \frac{0.8329}{2.301}

cos (A) = \frac{0.8329}{2.301}

Apply trig inverse properties

cos (A) = \frac{0.8329}{2.301}

General solutions for

cos (A) = \frac{0.8329}{2.301}

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

A = arccos (\frac{0.8329}{2.301}) + 2 πn, A = 2 π - arccos (\frac{0.8329}{2.301}) + 2 πn

A = arccos (\frac{0.8329}{2.301}) + 2 πn, A = 2 π - arccos (\frac{0.8329}{2.301}) + 2 πn

Show solutions in decimal form

A = 1.20041 \dots + 2 πn, A = 2 π - 1.20041 \dots + 2 πn

Graph

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