A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{2}$ $(pi)/2$ . If side C has a length of $18$ $18$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what is the length of side A?

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Answer 1 · 2017-11-17T11:05:20

Length of side $A$ $A$ is $4.66 (2 d p)$ $4.66(2dp)$ unit.

Angle between Sides $A and B$ $A and B$ is $∠ c = \frac{π}{2} = \frac{180}{2} = 90^{0}$ $/_c= pi/2=180/2=90^0$

Angle between Sides $B and C$ $B and C$ is $/_a= pi/12=180/12=15^0 :.$

Angle between Sides $C and A$ is $/_b= 180-(90+15)=75^0$

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

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

$A/sina = B/sinb=C/sinc ; C=18 :. A/sina=C/sinc$ or

$A/sin15=18/sin90 :. A = 18* sin15/sin90 ~~ 4.66(2dp)$ unit

Length of side $A$ is $4.66(2dp)$ unit. [Ans]

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/2π2(pi)/2. If side C has a length of 18 1818 and the angle between sides B and C is pi/12π12pi/12, what is the length of side A?