A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $(pi)/4$ . If side C has a length of $25$ $25$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2018-04-11T11:28:02

$Length of side = a = b = 6.53 units$ $color(indigo)("Length of side " = a = b = 6.53 " units"$

$ˆ A = \frac{3 π}{8}, ˆ C = \frac{π}{4}, c = 25, To find a & b$ $hat A = (3pi)/8, hat C = pi/4, c = 25, " To find a & b"$

$ˆ B = π - \frac{3 π}{8} - \frac{π}{4} = \frac{3 π}{8}$ $hat B = pi - (3pi)/8 - pi / 4 = (3pi) / 8$

It's an isosceles triangle with sides a & b equal.

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

$:. a = b = (c * sin B) / sin C = (25 * sin ((3pi)/8)) / sin (pi/4)$

$color(indigo)(a = b = 6.53 " units"$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/4π4(pi)/4. If side C has a length of 25 2525 and the angle between sides B and C is ( 3 pi)/83π8( 3 pi)/8, what are the lengths of sides A and B?