A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-05-31T11:59:53

Largest possible area of the triangle is

$A_{t} = 2.59$ $A_t = color(crimson)(2.59$ sq units

Explanation:

$ˆ A = \frac{π}{6}, ˆ B = \frac{3 π}{8}, ˆ C = \frac{11 π}{24}$ $hat A = pi/6, hat B = (3pi)/8, hat C =(11pi)/24$

Side ‘2’ should correspond to the least angle $ˆ A = \frac{π}{6}$ $hat A = pi/6$

According to the law of Sines,

$b = \frac{a sin B}{sin A} = \frac{2 \cdot sin (\frac{3 π}{8})}{sin (\frac{π}{4})} = 2.61$ $b = (a sin B) / sin A = (2 * sin ((3pi)/8)) / sin (pi/4) = 2.61$

Largest possible area of the triangle is

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

$A_{t} = (\frac{1}{2}) \cdot 2 \cdot 2.61 \cdot sin (\frac{11 π}{24}) = 2.59$ $A_t = (1/2) * 2 * 2.61 * sin ((11pi)/24) = color(crimson)(2.59$ sq units

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A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of π6 pi / 6 and 3π8 (3 pi )/ 8 . If one side of the triangle has a length of 22 , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{6}$ $pi / 6$ and $\frac{3 π}{8}$ $(3 pi )/ 8$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?