A triangle has two corners with angles of $\frac{π}{2}$ $( pi ) / 2$ and $\frac{5 π}{12}$ $( 5 pi )/ 12$ . 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 · 2017-12-11T05:20:21

Largest possible area of the triangle is 1.866

Given are the two angles $\frac{π}{2}$ $(pi)/2$ and $5 \frac{π}{12}$ $5pi/12$ and the length 1

The remaining angle:

$= π - (\frac{π}{2}) + (5 \frac{π}{12}) = \frac{π}{12}$ $= pi - ((pi)/2) + (5pi/12) = (pi)/12$

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 $= \frac{1^{2} \cdot sin (\frac{π}{2}) \cdot sin (\frac{5 π}{12})}{2 \cdot sin (\frac{π}{12})}$ $=( 1^2*sin(pi/2)*sin((5pi)/12))/(2*sin(pi/12))$

Area $= 1.866$ $=1.866$

A triangle has two corners with angles of ( pi ) / 2 π2 ( pi ) / 2 and ( 5 pi )/ 12 5π12 ( 5 pi )/ 12 . If one side of the triangle has a length of 1 11 , what is the largest possible area of the triangle?