Find the measure of angle A

Mathematics

1 answer:

sukhopar [10]3 years ago

8 0

Angle A has a length of 117

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Sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).

Sever21 [200]

$\sin(\alpha-\beta)=\sin\alpha\cos\beta-\cos\alpha\sin\beta$

$\sin\alpha=\dfrac{21}{29}\implies \cos^2\alpha=1-\sin^2\alpha=\dfrac{400}{841}$

Since $\alpha$ lies in quadrant II, we have $\cos\alpha$ , so

$\cos\alpha=-\sqrt{\dfrac{400}{841}}=-\dfrac{20}{29}$

$\cos\beta=\dfrac{15}{17}\implies\sin^2\beta=1-\cos^2\beta=\dfrac{64}{289}$

$\beta$ lies in quadrant I, so $\sin\beta>0$ and

$\sin\beta=\sqrt{\dfrac{64}{289}}=\dfrac8{17}$

So

$\sin(\alpha-\beta)=\dfrac{21}{29}\dfrac{15}{17}-\left(-\dfrac{20}{29}\right)\dfrac8{17}=\dfrac{475}{493}$

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