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 sidesA and B is
color(red)(angleM)
Name the angles between sidesB and C is
color(brown)(angleN)

GIVEN:
color(red)(angleM=pi/2)
color(brown)(angleN=pi/12)
sideB=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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