A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T12:18:46

Largest possible area of the triangle is 2.2497

Explanation:

Given are the two angles $\frac{7 π}{12}$ $(7pi)/12$ and $\frac{π}{4}$ $pi/4$ and the length 2

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

Area $= 2.2497$ $=2.2497$

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A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?