Question

A triangular piece of commercial real estate is priced at $5.75 per square foot. Determine the cost of the triangular piece of land if two sides of the lot measure 140 feet by 200 feet and the angle between these two sides is 60 The cost of the property is (Round to the nearest dollar as needed.)

Answer 1

Cost= 69,713 $

Explanation:

as we have two sides and an angle we apply the law of cosine

`a^(2)=b^(2)+c^(2)-2bc*cosA\\a^(2)=140^(2)+200^(2)-2*140*200*cos60\\a^(2)=19600+40000-56000*0.5\\a^(2)=31600;a=√(31600)=177.76`,

we must find h, so

`sin60=(H)/(b)`

`H=b*sin60=140*(√(3))/(2)=121.24`

finally

`A_(lt)=(b*h)/(2)=(200*121.24)/(2)=12,124ft^(2)`

the cost of the triangle piece of land is:

Cost=5.75 $/ft2 * 12.124ft2 = 69,713 $