A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/12#. If side B has a length of 27, what is the area of the triangle?

1 Answer
Mia
Oct 22, 2016

#Area triangle = 97.66#

Explanation:

Name the angles between sides#A and B # is
#color(red)(angleM)#
Name the angles between sides#B and C # is
#color(brown)(angleN)#

GIVEN:
#color(red)(angleM=pi/2)#
#color(brown)(angleN=pi/12)#
side#B=27#

Let us find the area of this triangle:
The given #triangle# is right at M because #color(red)(angleM=pi/2)#

#color(blue)(Area=(b*h)/2)#
so,
base #color(blue)b=B=27#
height #color(blue)h=color(green)A=???#

#color(blue)(Area=(27*color(green)A)/2)#

Let us find side #color(green)A=???#
side #A# is opposite to #color(brown)(angleN)#
Since given the adjacent side #B# to the angle #color(brown)(angleN)#

#color(purple)(tanN=A/B)#
#tan(pi/12)=A/B#
#tan(pi/12)=A/27#
#A=tan(pi/12)*27#

#color(green)(A=7.235)#

Therefore,
#color(blue)(Area=(27*color(green)A)/2)#
#color(blue)(Area=(27*color(green)7.235)/2)#
#color(blue)(Area=97.66)#

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