Find the measure of the indicated angle to the nearest degree
1 answer:
You can use the sine law, which states that, in every triangle, the ratio between a side and the sine of the opposite angle is constant.
So, we have
![\dfrac{59}{\sin(90)}=\dfrac{42}{\sin(x)}](https://tex.z-dn.net/?f=%5Cdfrac%7B59%7D%7B%5Csin%2890%29%7D%3D%5Cdfrac%7B42%7D%7B%5Csin%28x%29%7D)
where
is the angle you're looking for. Now, remember that
, and we can solve the equation for
:
![\sin(x)=\dfrac{42}{59}](https://tex.z-dn.net/?f=%5Csin%28x%29%3D%5Cdfrac%7B42%7D%7B59%7D)
Which implies that the angle itself is
![x=\arcsin\left(\dfrac{42}{59}\right)\approx 45.39](https://tex.z-dn.net/?f=x%3D%5Carcsin%5Cleft%28%5Cdfrac%7B42%7D%7B59%7D%5Cright%29%5Capprox%2045.39)
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Step-by-step explanation:
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Step-by-step explanation:
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Answer
x=-40
hope this helps and have a wonderful day :)