A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2#. If side C has a length of #23 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-07-15T08:25:02

The length of side #A# is #=5.95#

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The angle #hatC=1/2pi#

The angle #hatA=1/12pi#

The side #c=23#

The side #a=?#

We apply the sine rule to the triangle #DeltaABC#

#a/sin hat(A)=c/sin hat(C)#

#a=c*sin hat (A)/sin hat (C)#

#=23*sin(1/12pi)/sin(1/2pi)#

#=5.95#

Answer 2 · 2017-07-15T08:28:10

#a=#5.9528units

Use the Sine Law
#sinA/a=sinB/b=sinC/c#

Angle between A and B = angle C =#pi/2#
Angle between B and C = angle A =#pi/12#
c=23 units

#sin(pi/12)/a=sin(pi/2)/23#

#(23sin(pi/12))/sin(pi/2)=a#

#a=#5.9528units

Answer 3 · 2017-07-15T09:10:55

5.8 units

By your question its clearly identified that its a right angled triangle with side c as its hypotenuse.

The value of :-

#sin(pi/12) = (sqrt(3) - 1)/(2sqrt(2))#
#sqrt3 =1.71#
#sqrt2 = 1.41#

is to be remembered

So,
#A/23 = (sqrt(3) - 1)/(2sqrt(2))#

By calculating we get,
#A = 5.8 units#