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 $4$ $4$ 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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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 $4$ $4$ 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 · 2016-01-06T12:25:40

The final answer is A = B = $4 \cdot \sqrt{2}$ $4*sqrt(2)$

Explanation:

We have two angles $\frac{π}{4}$ $pi/4$ and $3 \frac{π}{8}$ $3pi/8$ so by adding them and subtracting the sum from $π$ $pi$ ( $π = 180$ $pi=180$ = the sum of the angles of a triangle). The third angle is $π - (3 \frac{π}{8} + \frac{π}{4})$ $pi - (3pi/8 + pi/4)$ = $3 \frac{π}{8}$ $3pi/8$ .

From the angles, we can infer that the triangle is isosceles, and we already know that $t h e ∠ b e t w e e n A and B = t h e ∠ b e t w e e n A and C$ $the angle between A and B = the angle between A and C$ , by exclusion (since $t h e ∠ b e t w e e n A and B \neq t h e ∠ b e t w e e n B and C$ $the angle between A and B!=the angle between B and C$ ). Therefore, A=B.
$sin ∠ b e t w e e n A and B = \frac{C}{A} = sin (\frac{π}{4}) = \frac{1}{\sqrt{2}}$ $sin /_ between A and B =C/A= sin (pi/4) = 1/sqrt(2)$
$\frac{4}{A} = \frac{1}{\sqrt{2}}$ $4/A = 1/sqrt(2)$

$A = 4 \cdot \sqrt{2}$ $A= 4*sqrt(2)$

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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 $4$ $4$ 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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A triangle has sides A, B, and C. The angle between sides A and B is π4(pi)/4. If side C has a length of 44 and the angle between sides B and C is 3π8( 3 pi)/8, what are the lengths of sides A and B?

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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 $4$ $4$ 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?