A triangle has two corners with angles of $\frac{π}{2}$ $pi / 2$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . 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 $\frac{π}{2}$ $pi / 2$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . 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 · 2018-01-09T05:10:14

Largest possible Area of Delta ABC = $A_{t} = 173.8236$ $A_t = color (red)(173.8236)$

Explanation:

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$C = \frac{π}{2}, B = \frac{3 π}{8}, A = π - \frac{π}{2} - \frac{3 π}{8} = \frac{π}{8}$ $C = pi / 2, B = (3pi)/8, A = pi - pi/2 - (3pi)/8 = pi / 8$

Side 12 should correspond to the smallest angle (pi/8) to get the largest possible area.

$\frac{12}{sin (\frac{π}{8})} = \frac{b}{sin (\frac{3 π}{8})} = \frac{c}{sin (\frac{π}{2})}$ $12 / sin (pi/8) = b / sin ((3pi) / 8) = c / sin (pi/2)$

$b = \frac{12 \cdot sin (\frac{3 π}{8})}{sin (\frac{π}{8})} = 28.9706$ $b = (12 * sin ((3pi)/8)) / sin (pi/8) = 28.9706$

$c = \frac{12 sin (\frac{π}{2})}{sin (\frac{π}{8})} = 31.3575$ $c = (12sin(pi/2)) / sin (pi/8) = 31.3575$

Largest possible area of Delta ABC = $A_{t} = (\frac{1}{2}) b a = (\frac{1}{2}) \cdot 28.9706 \cdot 12 = 173.8236$ $A_t = (1/2) b a = (1/2) * 28.9706 * 12 = color (red)(173.8236)$

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A triangle has two corners with angles of $\frac{π}{2}$ $pi / 2$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . If one side of the triangle has a length of $12$ $12$ , what is the largest possible area of the triangle?

1 Answer

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A triangle has two corners with angles of pi / 2 π2 pi / 2 and (3 pi )/ 8 3π8 (3 pi )/ 8 . If one side of the triangle has a length of 12 1212 , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{2}$ $pi / 2$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . If one side of the triangle has a length of $12$ $12$ , what is the largest possible area of the triangle?