A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , 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 $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-05-12T03:58:50

$Largest possible Area of triangle A_{t} = 12.5 sq units$ $color(maroon)("Largest possible Area of triangle " A_t = 12.5 " sq units"$

Explanation:

$ˆ A = \frac{π}{12}, ˆ B = \frac{5 π}{8}, ˆ C = π - \frac{π}{12} - \frac{5 π}{8} = \frac{7 π}{24}$ $hat A = pi/12, hat B = (5pi) / 8, hat C = pi - pi/12 - (5pi) / 8 = (7pi)/24$

To get the largest area, side 3 should correspond to least angle $ˆ A$ $hatA$

Applying the Law of Sines,

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a / sin A = b / sin B = c / sin C$

$\frac{3}{sin (\frac{π}{12})} = \frac{b}{sin (\frac{5 π}{8})}$ $3 / sin (pi/12) = b / sin ((5pi)/8)$

$b = \frac{3 \cdot sin (\frac{5 π}{8})}{sin (\frac{π}{12})} = 10.71$ $b = (3 * sin ((5pi)/8)) / sin (pi/12) = 10.71$

$Area of Triangle A_{t} = (\frac{1}{2}) a b sin C$ $"Area of Triangle " A_t = (1/2) a b sin C$

$A_{t} = (\frac{1}{2}) \cdot 3 \cdot 10.71 \cdot sin (\frac{7 π}{24}) = 12.5 sq units$ $A_t = (1/2) * 3 * 10.71 * sin ((7pi)/24) = 12.5 " sq units"$

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A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of π12 pi / 12 and 5π8 (5 pi )/ 8 . If one side of the triangle has a length of 33 , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $3$ $3$ , what is the largest possible area of the triangle?