If sides A and B of a triangle have lengths of 8 and 5 respectively, and the angle between them is #(pi)/3#, then what is the area of the triangle?

2 Answers

#Area=10 sqrt(3)# square units

Explanation:

Use the formula #Area=1/2*ab sin C# OR
#Area=1/2*bc sin A# OR
#Area=1/2*ac sin B#
In this case side #a=8#, side #b=5#, angle #C=pi/3#

#Area= 1/2 ab sin C#
#Area=1/2* 8*5*sin (pi/3)#

#Area=1/2*8*5*sqrt3/2#

#Area=10 sqrt(3)# square units

Jan 22, 2016

# 10sqrt3 #

Explanation:

In a triangle with 2 known sides , say a , and b , and the angle between them is #theta #

then area (A) = # 1/2 ab sintheta #

In this question a = 8 , b = 5 and # theta = pi/3 #

# rArr A = 1/2 xx 8 xx 5 xx sin(pi/3) = 20 xx sqrt3/2 = 10sqrt3 #