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 $15$ $15$ , 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 $15$ $15$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-06-25T10:30:20

The longest perimeter is $= 61.6$ $=61.6$

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 $15$ $15$ in font of the smallest angle, i.e. $\frac{5}{24} π$ $5/24pi$

We apply the sine rule

$\frac{A}{sin (\frac{5}{12} π)} = \frac{B}{sin (\frac{3}{8} π)} = \frac{15}{sin (\frac{5}{24} π)} = 24.64$ $A/sin(5/12pi)=B/sin(3/8pi)=15/sin(5/24pi)=24.64$

$A = 24.64 \cdot sin (\frac{5}{12} π) = 23.8$ $A=24.64*sin(5/12pi)=23.8$

$B = 24.64 \cdot sin (\frac{3}{8} π) = 22.8$ $B=24.64*sin(3/8pi)=22.8$

The perimeter is

$P = 15 + 23.8 + 22.8 = 61.6$ $P=15+23.8+22.8=61.6$

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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 $15$ $15$ , 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 5π12 (5 pi )/ 12 and 3π8 (3 pi ) / 8 . If one side of the triangle has a length of 15 15 , 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 $\frac{3 π}{8}$ $(3 pi ) / 8$ . If one side of the triangle has a length of $15$ $15$ , what is the longest possible perimeter of the triangle?