Question

Can you calculate the following?

Calculate the exact area of `DeltaABC`

Answer 1

`7.5sqrt(3)` `m^2`

Explanation:

From the diagram:

Using `/_BCA` and side `AC`

Altitude of triangle is:

`5sin(60)`

Using base `BC`

Area a triangle is:

`1/2"base" xx "height"`

`:.`

`1/2BC*5sin(60)`

`1/2*6*5sin(60)`

`sin(60)=sqrt(3)/2`

`1/2*6*5sqrt(3)/2=7.5sqrt(3)` `m^2`

Answer 2

The Area of `DeltaABC=1/2*a*b*sinC=1/2*6*5*sqrt3/2`,
`=7.5sqrt3~~12.99 m^2`.