A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $5$ $5$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T13:02:35

Largest possible area of the triangle is 29.5753

Given are the two angles $\frac{π}{12}$ $(pi)/12$ and $\frac{π}{4}$ $pi/4$ and the length 5

The remaining angle:

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

I am assuming that length AB (5) 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 $= \frac{5^{2} \cdot sin (\frac{π}{4}) \cdot sin (\frac{2 p}{3})}{2 \cdot sin (\frac{π}{12})}$ $=( 5^2*sin(pi/4)*sin((2p)/3))/(2*sin(pi/12))$

Area $= 29.5753$ $=29.5753$

A triangle has two corners with angles of π12 pi / 12 and π4 pi / 4 . If one side of the triangle has a length of 55 , what is the largest possible area of the triangle?