What is the exact value of sin 2a [closed]

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The question says a right angled triangle has sides and angles shown in the diagram. What is the exact value of $\sin(2a)$?

Thanks diagram shows a right angled triangle with a hypotenuse of $\sqrt{34}$, an adjacent of $5$, an opposite side from the angle of $3$, and an angle of $a$.

I'm new to this so help will be appreciated

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1 Answer

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We can find $\sin(2a)$ by using the double angle identity $$\sin(2a) = 2\sin(a)\cos(a).$$ We see that $\sin(a)$ is just $3/\sqrt{34}$. The cosine of angle a is $\cos a=5/\sqrt{34}$. So $$\sin(2a) = 2 \times \frac{3}{\sqrt{34}}\times \frac{5}{\sqrt{34}} = \frac{15}{17}.$$

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