Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-08T12:23:15

Largest possible area of the triangle is 27.5587

Explanation:

Given are the two angles $\frac{5 π}{8}$ $(5pi)/8$ and $\frac{π}{6}$ $pi/6$ and the length 7

The remaining angle:

$= π - ((\frac{5 π}{8}) + \frac{π}{6}) = \frac{5 π}{24}$ $= pi - (((5pi)/8) + pi/6) = (5pi)/24$

I am assuming that length AB (1) is opposite the smallest angle.

Using the ASA

Area $= \frac{c^{2} \cdot sin (A) \cdot sin (B)}{2 \cdot sin (C)}$ $=(c^2*sin(A)*sin(B))/(2*sin(C)$

Area $= \frac{7^{2} \cdot sin (\frac{5 π}{24}) \cdot sin (\frac{5 π}{8})}{2 \cdot sin (\frac{π}{6})}$ $=( 7^2*sin((5pi)/24)*sin((5pi)/8))/(2*sin(pi/6))$

Area $= 27.5587$ $=27.5587$

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $7$ $7$ , 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 5π8 (5 pi )/ 8 and π6 ( pi ) / 6 . If one side of the triangle has a length of 7 7 , what is the longest possible perimeter of the triangle?

1 Answer

Explanation:

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Impact of this question

Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{6}$ $( pi ) / 6$ . If one side of the triangle has a length of $7$ $7$ , what is the longest possible perimeter of the triangle?