Find the area of a triangular parcel of land using the concept of trigonometry

Question

Goal: Your task is to survey the area of a triangular parcel of land using the concept of trigonometry.

Role: You are a surveyor.

Audience: The target audience is the prospective buyers of the land.

Three prospective buyers of the triangular parcel of land are interested in buying the land. All of the prospective buyers want the land so much because each side of the land is along a road which makes the land very accessible. The only thing that keeps them from buying the land is that they do not know the area of the land:

Prospective buyer no. 1 wants the area to be within the range of 500 𝑚2 to 750 𝑚2 ;

Prospective buyer no. 2 wants the area to be within the range of 750 𝑚2 to 850 𝑚2 ;

and Prospective buyer no. 3 wants the area to be exactly 850 𝑚2 .

To make sure that the area of the land is what they wanted, they agreed to hire you as a surveyor and share the expenses for your fee.

Product/Performance: You will sketch a land drawn to scale and computations indicating the area of the triangle.

Answer 1

Since this problem gives no dimensions, the dimensions are up to you.

You simply need to remember how to compute the area of a triangle: either (1/2) base * height or

(1/2) the product of any 2 sides * the sin of the angle between them.