Two corners of a triangle have angles of $\frac{3 π}{8}$ $(3 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{3 π}{8}$ $(3 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-10-08T22:44:52

Per $= 50.5838$ $=50.5838$

Explanation:

Three angles are $\frac{π}{4}, \frac{3 π}{8}, \frac{3 π}{8}$ $pi/4,(3pi)/8,(3pi)/8$
$\frac{a}{sin a} = \frac{b}{sin b} = \frac{c}{sin c}$ $a/sin a=b/sin b=c/sin c$
$\frac{a}{sin (\frac{π}{4})} = b sin (\frac{3 π}{8}) = \frac{c}{sin (\frac{3 π}{8})}$ $a/sin (pi/4)=bsin ((3pi)/8)=c/sin ((3pi)/8)$
$\frac{14}{sin (\frac{3 π}{8})} = \frac{14}{sin (\frac{π}{4})}$ $14/sin ((3pi)/8)=14/sin (pi/4)$
$b = \frac{14 \cdot sin (\frac{3 π}{8})}{sin (\frac{π}{4})}$ $b=(14*sin ((3pi)/8))/sin(pi/4)$
$b = \frac{14 \cdot 0.9239}{0.7071} = 18.2919$ $b=(14*0.9239)/0.7071=18.2919$
$c = \frac{14 \cdot sin (\frac{3 π}{8})}{sin (\frac{π}{4})}$ $c=(14*sin((3pi)/8))/sin(pi/4)$
$c = \frac{14 \cdot 0.9239}{0.7071} = 18.2919$ $c=(14*0.9239)/0.7071=18.2919$
Perimeter $= 14 + 18.2919 + 18.2919 = 50.5838$ $=14+18.2919+18.2919=50.5838$

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Two corners of a triangle have angles of $\frac{3 π}{8}$ $(3 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Science

Math

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Two corners of a triangle have angles of 3π8 (3 pi )/ 8 and π4 ( pi ) / 4 . If one side of the triangle has a length of 14 14 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Two corners of a triangle have angles of $\frac{3 π}{8}$ $(3 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?