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 · 2018-01-24T08:36:51

Area of the triangle $Delta ABC = (1/2) * 8 * 13.8564 = color(blue)(55.4256)$ sq. units

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Three angles of the triangle are $alpha = pi/3, beta = pi/6, gamma = pi - (pi/3 + pi/6) = pi/2$

It’s a right triangle with sides in the ratio $1 : sqrt3 :2$ , length ‘2’ being the hypotenuse.

To get the maximum area, length ‘8’ should correspond to the smallest angle $pi/6$ .

Hence the sides are $8, 8sqrt3, 8*2$

I.e. $8, 13.8564, 16$

Area of the triangle $Delta ABC = (1/2) * 8 * 13.8564 = color(blue)(55.4256)$ sq. units

A triangle has two corners with angles of ( pi ) / 3 π3 ( pi ) / 3 and ( pi )/ 6 π6 ( pi )/ 6 . If one side of the triangle has a length of 8 88 , what is the largest possible area of the triangle?