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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

enter image description here

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closed as off-topic by JonMark Perry, colormegone, Leucippus, user223391, user236182 Jan 7 '16 at 0:23

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  • $\begingroup$ Sorry, that should be sqrt (34), I'll edit it $\endgroup$ – finlx Jan 6 '16 at 22:59
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    $\begingroup$ HINT: Use the identity:$$\sin(2a)=2\sin(a)\cos(a)$$ $\endgroup$ – Mufasa Jan 6 '16 at 23:00
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    $\begingroup$ I have added my own diagram to the question. $\endgroup$ – user236182 Jan 6 '16 at 23:13
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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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