precalc homework

Question

A triangular lot has sides of lengths 327 feet, 180 feet, and 202 feet. Find the area of the lot. (Round your answer to one decimal place.)

Answer 1

 

Hi Emi,

 

Let a = 180, b = 327, and c = 202.

 

From the cosine rule,

 

     cos(C) = (a² + b² - c²)/(2ab)

 

               = (180² + 327² - 202²)/(2·180·327)

 

               = 0.8369

 

The area of the triangle is

 

     Area = (1/2)·a·b·sin(C)

 

             = (1/2)·a·b·√(1 - cos²(C))

 

             = (1/2)·180·327·√(1 - 0.8369²)

 

             = 16,108.7