Answer:
5. 77.32°
6. 54.46°
7. 13.6
8. 19.5
9. 6.5
10. 12.6
Step-by-step explanation:
I find the mnemonic SOH CAH TOA to be extremely helpful for problems like this. It reminds you ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Tan = Opposite/Adjacent
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Based on your notes of problems 5 ad 6, I'd say you need to be a little careful of notation. The relationship between angles and side ratios is ...
• TrigFunction(angle) = ratio . . . . . . . . trig functions are sin, cos, tan, csc, sec, cot
• InverseTrigFunction(ratio) = angle . . . inverse trig functions are arcsin, arccos, arctan, arccsc, arcsec, arccot. These are also written with a -1 superscript, for example, sin⁻¹ for arcsin.
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5. sin(x°) = 40/41 . . . . . . . . . . . . opposite/hypotenuse
x° = arcsin(40/41) ≈ 77.32°
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6. tan(x°) = 7/5 . . . . . . . . . . . . . . opposite/adjacent
x° = arctan(7/5) ≈ 54.46°
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7. tan(39°) = 11/x
x = 11/tan(39°) . . . . . . . . . multiply both sides of the equation by x/tan(39°)
x ≈ 13.6
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8. cos(46°) = x/28
x = 28·cos(46°) ≈ 19.5
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9. tan(51°) = 8/x
x = 8/tan(51°) ≈ 6.5 . . . . . solve as in problem 7
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10. sin(24°) = x/31
x = 31·sin(24°) ≈ 12.6
