Question

Please help?

Answer 1

The area of the triangle is `84ft^2`

Explanation:

Calculating the height of the triangle
`sin 30^0 = h/16`

`h = 0.5*16 = 8`

The area is of a triangle is given by `1/2*`base`*`height
from the diagram the base is 21ft
from the previous calculation the height is 8ft

`1/2*8*21 = 84`

The area of the triangle is `84ft^2`

If you are confused of why this calculation is true, look at the image below:

Answer 2

`A~~83.9977`

Explanation:

We use the Laws of Cosines, which states that:
`a^2=b^2+c^2-2bc*cos(alpha)` where `a` and `alpha` are opposite to each other.

Therefore,
`b=16`
`c=21`
`alpha=30`

We now have:

`a^2=16^2+21^2-2*16*21*cos(30)`

=>`a^2=256+441-cancel672*sqrt3/cancel2`

=>`a^2=697-336*sqrt3`

=>`a=sqrt (697-336*sqrt3 )` Notice that `a` can only be positive.

=>`a~~10.725`

Now, we use the Heron's Formula, which states that:

`A=sqrt(s(s-a)(s-b)(s-c))` where `s=(a+b+c)/2`

Therefore,

`s=(10.725+16+21)/2`

=>`s=23.8625`

We plug in the values.

`A=sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(23.8625(23.8625-10.725)(23.8625-16)(23.8625-21))`

`~~83.9977`