Question

Texas rancher wants to fence off his four-sided plot of flat land. He measures the first three sides, shown as A, B, and C in the figure below, where

A = 4.15 km

and

?_C = 23°.

He then correctly calculates the length in kilometers and orientation in degrees west of south of the fourth side D. What is his result in kilometers and degrees west of south?

A= 4.15km corresponding degrees is 7.5

B= 2.48 and corresponding degrees is 16

C= 3.02 km and degrees is 23

Answer 1

We know that, + + + = 0

= - - -

On the x-axis, we have

D_x = - (A_x + B_x + C_x)

D_x = - [(4.15 km) cos 7.5⁰ + (-2.48 km) sin 16⁰ + (-3.02 km) cos 23⁰]

D_x = - (0.6509 km)

On y-axis, we have

D_y = - (A_y + B_y + C_y)

D_y = - [(-4.15 km) sin 7.5⁰ + (2.48 km) cos 16⁰ + (3.02 km) sin 23⁰]

D_y = - (3.02 km)

Magnitide of the length, D which will be given as :

| D | = D_x² + D_y²

| D | = (-0.6509 km)² + (-3.02 km)²

| D | = 3.08 km

The orientation of fourth side D which will be given by -

using a trigonometric identity, we have

= tan^-1 [(-0.6509 km) / (-3.02 km)]

= tan^-1 (0.2155)

= 12.1 degree

{ west of south }