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 $6$ $6$ , 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 $6$ $6$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2016-08-14T15:17:38

$= 13.35$ $=13.35$

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 $s i d e = h y p o t e n u s e = 6$ $side=hypoten use =6$ ;So other sides $= 6 sin (\frac{π}{12}) and 6 cos (\frac{π}{12})$ $=6sin(pi/12) and 6cos( pi/12)$

Therefore Perimeter of the triangle $= 6 + 6 sin (\frac{π}{12}) + 6 cos (\frac{π}{12})$ $=6+6sin(pi/12)+ 6cos( pi/12)$
$= 6 + (6 \times 0.2588) + (6 \times 0.966)$ $=6+(6times0.2588)+(6times0.966)$
$= 6 + 1.55 + 5.8)$ $=6+1.55+5.8)$
$= 13.35$ $=13.35$

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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 $6$ $6$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

Two corners of a triangle have angles of 5π12 (5 pi )/ 12 and π12 ( pi ) / 12 . If one side of the triangle has a length of 6 6 , what is the longest possible perimeter of the triangle?

1 Answer

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 $6$ $6$ , what is the longest possible perimeter of the triangle?