Answer: Choice C
sin(26) = x/10
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Explanation:
With respect to the 26 degree angle, the x is the opposite side and the 9 is the length of the adjacent side.
We can say tan(26) = x/9 because tangent is the ratio of opposite over adjacent. In other words, tan(angle) = opposite/adjacent
Unfortunately, tan(26) = x/9 is not an answer choice.
Luckily though, we have other trig ratios to work with.
The sine ratio ties together the opposite side and hypotenuse
sin(angle) = opposite/hypotenuse
sin(26) = x/10
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Extra info (optional section)
Solving for x leads to...
sin(26) = x/10
10*sin(26) = x
x = 10*sin(26)
x = 4.38371 approximately
Also, note how cos(26) = 0.89879 approximately, which is fairly close to 9/10 = 0.9. This indicates some rounding error is going on when your teacher is displaying either the 9, the 10, or the 26 degree angle.
