A landowner has a triangular piece of land that she wants to fence. Starting at the west-most corner, the first side to be A=70m long and the next side to be 𝐵=95m long. What is her result?

Question

A new landowner has a triangular piece of land that she wishes to fence. Starting at the west-most corner she measures the first side to be 𝐴=70mA=70m long and the next side to be 𝐵=95mB=95m long as shown in the figure below. She correctly calculates the length and orientation of the third side. What is her result? Include units as appropriate below.

Answer 1

This is a vector addition problem. C=A+B Solve the x- and y-component separately.

In general, for any vector A, Ax=A cos u, Ay=A sin u.

Here u has to be the angle relative to the +x axis.

So in this problem, the angle for vector A is -21, vector B is 90+11=101.

Cx=70 cos-21 + 95 cos 101

Cy = 70 sin-21 + 95 sin101

Then use Pythagorean theorem C = sqrt (Cx^2 + Cy^2)