Trigonometry show work

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  3. x = 39°; other angle is 51°

  4a. x = 4.1 cm

  4b. x = 16.9 cm

Step-by-step explanation:

Ordinarily, I'd start with SOH CAH TOA, which gives you the relations you use to get the formula for the solution. Since you want to start with the formula, we'll do that.

3. x = arcsin(opposite/hypotenuse) = arcsin((5 cm)/(8 cm)) ≈ 39°.

The other missing angle is its complement, 90° -39° = 51°.

The missing angles are x = 39°, and 51°.

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4a. adjacent = opposite/tan(angle)

  x = (8 cm)/tan(63°) ≈ 4.1 cm

x is about 4.1 cm.

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4b. adjacent = hypotenuse · cos(angle)

  x = (40 cm)cos(65°) ≈ 16.9 cm

x is about 16.9 cm

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step-by-step explanation:

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b. x + 1

step-by-step explanation:

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