# If sides A and B of a triangle have lengths of 2 and 9 respectively, and the angle between them is #(5pi)/6#, then what is the area of the triangle?

##### 1 Answer

Aug 27, 2016

4.5 square units.

#### Explanation:

Given a triangle, where 2 sides and the angle between them are known, as in this question. Then we can calculate the area (A) of the triangle using.

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(A=1/2xxaxxbxxsin("angle between them"))color(white)(a/a)|)))#

where a and b are the 2 known sides.here a = 2 , b = 9 and angle between them

#=(5pi)/6#

#rArrA=1/2xx2xx9xxsin((5pi)/6)#

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(sin((5pi)/6)=sin(pi-(5pi)/6)=sin(pi/6)=1/2)color(white)(a/a)|)))#

#rArrA=1/2xx2xx9xxsin(pi/6)#

#rArrA=1/2xx2xx9xx1/2=4.5" square units"#