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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:

Parabola

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#