Question

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?

Answer 1

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"`