A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $5$ $5$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $5$ $5$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-05-31T12:12:34

Largest possible area of the triangle is

$A_{t} = 21.34$ $A_t = color(green)(21.34$

Explanation:

$ˆ A = \frac{π}{4}, ˆ B = \frac{π}{8}, ˆ C = π - \frac{π}{4} - \frac{π}{8} = \frac{5 π}{8}$ $hat A = pi/4, hat B = pi/8, hat C = pi - pi/4 - pi/8 = (5pi)/8$

Side 5 should correspond to least angle $ˆ B$ $hatB$ to get the largest area of the triangle.

As per Law of Sines, $a = \frac{b sin A}{sin B}$ $a = (b sin A) / sin B$

$a = \frac{5 \cdot sin (\frac{π}{4})}{sin (\frac{π}{8})} = 9.24$ $a = (5 * sin (pi/4)) / sin (pi/8) = 9.24$

Largest possible area of the triangle is

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

$A_{t} = (\frac{1}{2}) (5 \cdot 9.24 \cdot sin (\frac{5 π}{8})) = 21.34$ $A_t = (1/2) (5 * 9.24 * sin ((5pi)/8)) = color(green)(21.34$

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A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $5$ $5$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of π4 pi / 4 and π8 pi / 8 . If one side of the triangle has a length of 55 , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{8}$ $pi / 8$ . If one side of the triangle has a length of $5$ $5$ , what is the largest possible area of the triangle?