Question

5 a surveyor is drawing property lines. he draws one line that is 25.0 meters long and is 20° south of west. how long is the western component of the vector he has drawn? 8.55 m 21.1 m 23.5 m 9.10 m

Explanation:

Step1: Identify the formula for the component

The formula for the \(x\) - component (western component here) of a vector \(\vec{A}\) with magnitude \(A\) and angle \(\theta\) with respect to the \(x\) - axis is \(A_x = A\cos\theta\). Here, \(A = 25.0\space m\) and \(\theta=20^{\circ}\) (south of west, so the angle with the west - axis is \(20^{\circ}\)).

Step2: Calculate the western component

Substitute the values into the formula: \(A_x=25.0\times\cos(20^{\circ})\).
We know that \(\cos(20^{\circ})\approx0.9397\).
So, \(A_x = 25.0\times0.9397=23.4925\approx23.5\space m\)

Answer:

23.5 m