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Let's say two right angled triangles share a common hypotenuse which measures 10 in length and share an angle which measures $20^\circ$ in total. How do I work out the value of x (the side adjacent to the $20^\circ$ angle)? Using $\cos$ looks like the right strategy to apply but not sure how to proceed...

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jaykirby
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    That seems about correct. It'd be nice if we could see the actual diagram though. Are the two triangles congruent? Since they "share" the angle $20^\circ$, does the hypotenuse bisect the angle such that each right triangle has an interior angle of $10^\circ$? – Adriano Jun 19 '13 at 07:27
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    i think it will a rectangle which is divided in two right angle triangle by one of its diagonal which is common hypotaneous of both triangles.but i don't get line "share an angle $20^\circ$" – iostream007 Jun 19 '13 at 07:29
  • Thanks, I've just loaded the diagram in question. – jaykirby Jun 19 '13 at 08:53

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As has been commented, your question would benefit greatly from a diagram for clarity, but I believe I can answer it anyway.

Recall $\cos(\theta)=\frac{A}{H}$ so rearranging we get $A=H\cos(\theta)$ and now you just have to substitute in the appropriate values. In your diagram, you should be able to see, by symmetry, that the angle inside each triangle will be half of the $20^\circ$ so we have $H=10, \theta=10^\circ$

john
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  • Thanks, I've just loaded the diagram. Hope it makes things clearer. – jaykirby Jun 19 '13 at 08:56
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    I have edited my answer in response. – john Jun 19 '13 at 09:00
  • Could you please elaborate on how we can see by symmetry that the angle inside each triangle will be half of 20? Is there another way to reach the same conclusion? – jaykirby Jun 19 '13 at 09:20
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    well the two triangles each have same hypotenuse and as one of the sides for each triangle is the radius of the circle, these sides also have the same length and since they're right angled triangles, by Pythagoras's Theorem, the remaining sides are also the same length so the triangles are congruent. – john Jun 19 '13 at 09:58