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 $1$ $1$ 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 · 2018-06-04T12:01:55

Length of sides $A and B$ $A and B$ are $1.31$ $1.31$ unit each.

Angle between sides $A and B$ $A and B$ is $∠ c = \frac{π}{4} = \frac{180}{4} = 45^{0}$ $/_c= pi/4=180/4=45^0$

Angle between sides $B and C$ $B and C$ is $∠ a = \frac{3 π}{8} = \frac{540}{8} = {67.5}^{0}$ $/_a= (3pi)/8=540/8=67.5^0$

Angle between sides $C and A$ $C and A$ is

$∠ b = 180 - (45 + 67.5) = {67.5}^{0}$ $/_b= 180-(45+67.5)=67.5^0$ . This is an isosceles triangle.

The sine rule states if $A, B and C$ $A, B and C$ are the lengths of the sides

and opposite angles are $a, b and c$ $a, b and c$ in a triangle, then:

$A/sinA = B/sinb=C/sinc ; C=1 :. B/sin b=C/sin c$ or

$B/sin 67.5=1/sin 45 or B= 1* (sin 67.5/sin 45) ~~ 1.31 (2dp)$

Similarly $A/sina=C/sinc$ or

$A/sin 67.5=1/sin 45 or A= 1* (sin67.5/sin 45) ~~ 1.31 (2dp)$

Length of sides $A and B$ are $1.31$ unit each [Ans]

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 1 11 and the angle between sides B and C is ( 3 pi)/83π8( 3 pi)/8, what are the lengths of sides A and B?