A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $16$ $16$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $16$ $16$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-11T07:09:18

Largest possible area of the triangle is 115.2127

Explanation:

Given are the two angles $\frac{π}{8}$ $(pi)/8$ and $\frac{π}{8}$ $pi/8$ and the length 1

The remaining angle:

$= π - (\frac{π}{12}) + \frac{π}{8}) = \frac{19 π}{24}$ $= pi - ((pi)/12) + pi/8) = (19pi)/24$

I am assuming that length AB (12) 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 $= \frac{16^{2} \cdot sin (\frac{19 π}{24}) \cdot sin (\frac{π}{8})}{2 \cdot sin (\frac{π}{12})}$ $=( 16^2*sin((19pi)/24)*sin((pi)/8))/(2*sin(pi/12))$

Area $= 115.2127$ $=115.2127$

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A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $16$ $16$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of pi / 12 π12 pi / 12 and pi / 8 π8 pi / 8 . If one side of the triangle has a length of 16 1616 , what is the largest possible area of the triangle?

1 Answer

Explanation:

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Impact of this question

A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $16$ $16$ , what is the largest possible area of the triangle?