Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi ) / 12$ and $\frac{3 π}{8}$ $(3 pi ) / 8$ . If one side of the triangle has a length of $2$ $2$ , 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 $\frac{3 π}{8}$ $(3 pi ) / 8$ . If one side of the triangle has a length of $2$ $2$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-06-26T06:11:29

The perimeter is $= 8.32$ $=8.32$

Explanation:

The third angle of the triangle is

$= π - (\frac{5}{12} π + \frac{3}{8} π)$ $=pi-(5/12pi+3/8pi)$

$= π - (\frac{10}{24} π + \frac{9}{24} π)$ $=pi-(10/24pi+9/24pi)$

$= π - \frac{19}{24} π = \frac{5}{24} π$ $=pi-19/24pi=5/24pi$

The angles of the triangle in ascending order is

$\frac{5}{12} π > \frac{9}{24} π > \frac{5}{24} π$ $5/12pi>9/24pi>5/24pi$

To get longest perimeter, we place the side of length $2$ $2$ in front of the smallest angle, i.e. $\frac{5}{24} π$ $5/24pi$

We apply the sine rule

$\frac{A}{sin (\frac{5}{12} π)} = \frac{B}{sin (\frac{3}{8} π)} = \frac{2}{sin (\frac{5}{24} π)} = 3.29$ $A/sin(5/12pi)=B/sin(3/8pi)=2/sin(5/24pi)=3.29$

$A = 3.29 \cdot sin (\frac{5}{12} π) = 3.17$ $A=3.29*sin(5/12pi)=3.17$

$B = 3.29 \cdot sin (\frac{3}{8} π) = 3.03$ $B=3.29*sin(3/8pi)=3.03$

The perimeter is

$P = 2 + 3.29 + 3.03 = 8.32$ $P=2+3.29+3.03=8.32$

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Two corners of a triangle have angles of $\frac{5 π}{12}$ $(5 pi ) / 12$ and $\frac{3 π}{8}$ $(3 pi ) / 8$ . If one side of the triangle has a length of $2$ $2$ , 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 (5 pi ) / 12 5π12(5 pi ) / 12 and (3 pi ) / 8 3π8 (3 pi ) / 8 . If one side of the triangle has a length of 2 22 , 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 $\frac{3 π}{8}$ $(3 pi ) / 8$ . If one side of the triangle has a length of $2$ $2$ , what is the longest possible perimeter of the triangle?