A triangle has two corners with angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $( pi )/ 12$ . If one side of the triangle has a length of $4$ $4$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $( pi )/ 12$ . If one side of the triangle has a length of $4$ $4$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-05-31T09:52:29

Largest possible area of the triangle is

$A_{t} = 10.93$ $color(brown)(A_t = 10.93$ sq units

Explanation:

$ˆ A = \frac{3 π}{4}, ˆ B = \frac{π}{12}, ˆ C \equiv \frac{π}{6}$ $hat A = (3pi)/4, hat B = pi/12, hat C -= pi/6$

To get the largest area, side 4 should correspond to the least angle $(\frac{π}{12})$ $(pi/12)$

As per the Law of Sines,

$a = \frac{sin A \cdot b}{sin B} = \frac{sin (\frac{3 π}{4}) \cdot 4}{sin (\frac{π}{12})}$ $a = (sin A * b) / sin B = (sin ((3pi)/4) * 4) / sin (pi/12)$

$a = 10.93$ $a = 10.93$

Largest possible area of the triangle is

$A_{t} = (\frac{1}{2}) a b sin C = (\frac{1}{2}) \cdot 4 \cdot 10.93 \cdot sin (\frac{π}{6}) = 10.93$ $A_t = (1/2) a b sin C = (1/2) * 4 * 10.93 * sin (pi/6) = 10.93$

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A triangle has two corners with angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $( pi )/ 12$ . If one side of the triangle has a length of $4$ $4$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of 3π4 (3 pi ) / 4 and π12 ( pi )/ 12 . If one side of the triangle has a length of 44 , what is the largest possible area of the triangle?

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Explanation:

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A triangle has two corners with angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{12}$ $( pi )/ 12$ . If one side of the triangle has a length of $4$ $4$ , what is the largest possible area of the triangle?