A triangle has two corners with angles of $\frac{π}{3}$ $( pi ) / 3$ and $\frac{π}{6}$ $( pi )/ 6$ . If one side of the triangle has a length of $8$ $8$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T15:31:28

Largest possible area of the triangle is 55.4256

Given are the two angles $\frac{π}{3}$ $(pi)/3$ and $\frac{π}{6}$ $pi/6$ and the length 8

The remaining angle:

$= π - ((\frac{π}{6}) + \frac{π}{3}) = \frac{π}{2}$ $= pi - (((pi)/6) + pi/3) = (pi)/2$

I am assuming that length AB (8) 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 $= \frac{8^{2} \cdot sin (\frac{π}{2}) \cdot sin (\frac{π}{3})}{2 \cdot sin (\frac{π}{6})}$ $=( 8^2*sin(pi/2)*sin((pi)/3))/(2*sin(pi/6))$

Area $= 55.4256$ $=55.4256$

A triangle has two corners with angles of π3 ( pi ) / 3 and π6 ( pi )/ 6 . If one side of the triangle has a length of 88 , what is the largest possible area of the triangle?