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2 Answers
Feb 14, 2018

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:

ParabolaParabola

Feb 15, 2018

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