Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2016-08-16T12:17:45

$= 11.12$ $=11.12$

Explanation:

Clearly this is a right angled triangle as $π - \frac{5 π}{12} - \frac{π}{12} = \frac{π}{2}$ $pi-(5pi)/12-pi/12=pi/2$
One $s i d e = h y p o t e n u s e = 5$ $side=hypoten use =5$ ;So other sides $= 5 sin (\frac{π}{12}) and 5 cos (\frac{π}{12})$ $=5sin(pi/12) and 5cos( pi/12)$

Therefore Perimeter of the triangle $= 5 + 5 sin (\frac{π}{12}) + 5 cos (\frac{π}{12})$ $=5+5sin(pi/12)+ 5cos( pi/12)$

$= 5 + (5 \times 0.2588) + (5 \times 0.966)$ $=5+(5times0.2588)+(5times0.966)$

$= 5 + 1.3 + 4.83)$ $=5+1.3+4.83)$

$= 11.12$ $=11.12$

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?

1 Answer

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Two corners of a triangle have angles of (5 pi )/ 12 5π12 (5 pi )/ 12 and ( pi ) / 12 π12 ( pi ) / 12 . If one side of the triangle has a length of 5 5 5 , what is the longest possible perimeter of the triangle?

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Explanation:

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi )/ 12$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?