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

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

## closed as off-topic by JonMark Perry, colormegone, Leucippus, user223391, user236182Jan 7 '16 at 0:23

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – colormegone, Community, user236182
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• Sorry, that should be sqrt (34), I'll edit it – finlx Jan 6 '16 at 22:59
• HINT: Use the identity:$$\sin(2a)=2\sin(a)\cos(a)$$ – Mufasa Jan 6 '16 at 23:00
• I have added my own diagram to the question. – user236182 Jan 6 '16 at 23:13

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 $$\sin(2a) = 2 \times \frac{3}{\sqrt{34}}\times \frac{5}{\sqrt{34}} = \frac{15}{17}.$$