A triangle has sides A,B, and C. If the angle between sides A and B is #(pi)/3#, the angle between sides B and C is #pi/6#, and the length of B is 15, what is the area of the triangle?

2 Answers
Dec 23, 2017

this is a 30-60-90 angle triangle .
length of hypoteneuse is given that is #B=15#
using trignometry
#A=B×sin30° C=B×cos30°#
Area of #triangle# #ABC =A×C×1/2#
#=1/2×B×sin30°×B×cos30°#
#=1/2×B^2×1/2×sqrt3/2#
#=1/2×15^2×sqrt3/4#
#=1/2×225×sqrt3/8#
#~~48.7139289629#

Dec 23, 2017

#225sqrt(3)/8#

Explanation:

We know that #pi/6 "radians"=30^o# and #pi/6 "radians"=60^o#, so we are dealing with a 30-60-90 triangle.

If side B touches both the 30-degree angle and the 60-degree angle, then side B is opposite the 90-degree angle and is the hypotenuse of the triangle.

Since we know that the sides of a 30-60-90 triangle follow the pattern #x#-#xsqrt(3)#-#2x#, we can say that:

#2x=15#

#x=15/2#

#xsqrt(3)=15/2*sqrt(3)#

Now that we know the base and height of the triangle, we can find the area.

#"Area" = 1/2*(x)*(xsqrt(3))#

#=1/2*15/2*15/2*sqrt(3)#

#=225sqrt(3)/8#