A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $9$ $9$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T14:54:31

Largest possible area of the triangle is 69.1378

Given are the two angles $\frac{π}{4}$ $(pi)/4$ and $\frac{5 π}{8}$ $(5pi)/8$ and the length 9

The remaining angle:

$= π - (\frac{5 π}{8}) + \frac{π}{4}) = \frac{π}{8}$ $= pi - ((5pi)/8) + pi/4) = (pi)/8$

I am assuming that length AB (9) 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 $= \frac{9^{2} \cdot sin (\frac{π}{4}) \cdot sin (\frac{5 π}{8})}{2 \cdot sin (\frac{π}{8})}$ $=( 9^2*sin(pi/4)*sin((5pi)/8))/(2*sin(pi/8))$

Area $= 69.1378$ $=69.1378$

A triangle has two corners with angles of π4 pi / 4 and 5π8 (5 pi )/ 8 . If one side of the triangle has a length of 99 , what is the largest possible area of the triangle?