A triangle has two corners with angles of $\frac{2 π}{3}$ $(2 pi ) / 3$ and $\frac{π}{4}$ $( pi )/ 4$ . If one side of the triangle has a length of $1$ $1$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T13:57:49

Largest possible area of the triangle is 2.3458

Given are the two angles $\frac{2 π}{3}$ $(2pi)/3$ and $\frac{π}{4}$ $pi/4$ and the length 1

The remaining angle:

$= π - ((\frac{2 π}{3}) + \frac{π}{4}) = \frac{π}{12}$ $= pi - (((2pi)/3) + pi/4) = pi/12$

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 $= \frac{1^{2} \cdot sin (\frac{π}{4}) \cdot sin (\frac{2 π}{3})}{2 \cdot sin (\frac{π}{12})}$ $=( 1^2*sin(pi/4)*sin((2pi)/3))/(2*sin(pi/12)$

Area $= 2.3458$ $=2.3458$

A triangle has two corners with angles of 2π3 (2 pi ) / 3 and π4 ( pi )/ 4 . If one side of the triangle has a length of 11 , what is the largest possible area of the triangle?