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 $12$ $12$ , 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 $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $12$ $12$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-11T07:03:45

Largest possible area of the triangle is 170.3538

Explanation:

Given are the two angles $\frac{π}{12}$ $(pi)/12$ and $\frac{π}{4}$ $pi/4$ and the length 1

The remaining angle:

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

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 $= \frac{12^{2} \cdot sin (\frac{π}{4}) \cdot sin (\frac{2 π}{3})}{2 \cdot sin (\frac{π}{12})}$ $=( 12^2*sin((pi)/4)*sin((2pi)/3))/(2*sin(pi/12))$

Area $= 170.3538$ $=170.3538$

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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 $12$ $12$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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Science

Math

Humanities

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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 1212 , 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 $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $12$ $12$ , what is the largest possible area of the triangle?