Question 1206589
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Answer: <font color=red>1469.00508</font> (approximate)
Round this however your teacher instructs.


Explanation


There is a shortcut as ikleyn points out, but it's clear from the instructions that the teacher requires Heron's formula. 
I would follow the teacher's instructions to avoid losing points.


Heron's formula is only possible if we know all 3 sides of the triangle.


We're missing side 'a', but can find it using the Law of Cosines.
a^2 = b^2 + c^2 - 2*b*c*cos(A)
a^2 = 73^2 + 41^2 - 2*73*41*cos(79)
a^2 = 5867.817353676
a = sqrt(5867.817353676)
a = 76.60167983586
a = 76.60168
The result is approximate. 
Please make sure that your calculator is set to degrees mode. 



Now that we know all 3 sides, we can finally use Heron's formula.


The formula is:
A = sqrt(s*(s-a)*(s-b)*(s-c))
where,
s = semi perimeter = half the perimeter
s = (a+b+c)/2
s = (76.60168+73+41)/2
s = 95.30084
This value is approximate since 'a' was approximate.


Then,
A = sqrt(s*(s-a)*(s-b)*(s-c))
A = sqrt(95.30084*(95.30084-76.60168)*(95.30084-73)*(95.30084-41))
A = <font color=red>1469.00508</font>
This result is approximate. 
The precision will depend on the precision of variable 'a'.
Round the answer however your teacher instructs. 


I used GeoGebra to verify the answer. 
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