Question

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?

Answer 1

`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

Answer 2

`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`