91Ó°ÊÓ

As showing above fig-(measurement and angle )it is asked that the resultant displacement found from diagram.

There are three displacement figure A,B and C,assume that the y axis points to the north and x axis points to east.

$$\begin{gathered} \cos 45°=\frac{cx}{3.1} \\ Cx=3.1\cos 45°≈2.19 \\ \sin 45°=\frac{Cy}{3.1} \\ Cy=3.1Sin45°≈2.19 \end{gathered}$$

Vectors are

$$\begin{gathered} A=âŒ\copyright Ax,Ay〉=âŒ\copyright 0,2.6〉km \\ B=âŒ\copyright Bx,By〉=âŒ\copyright 4.0,0〉km \\ C=âŒ\copyright Cx,Cy〉=âŒ\copyright 3.1Cos45°,3.1Sin45°〉km \end{gathered}$$

R = A+B+C

R =$(0,2.6)+(4.0,0)+3.1Cos45,3.1Sin45)$

R =$(0+4.0+3.1Cos45,2.6+0+3.1Sin45)$

R$≈(6.19,4.79)km$…â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦.(1)

$\left|R\right|=\sqrt{(6.19{)}^2+(4.79{)}^2}$km ………….from equation (1)

$\mathbf{≈}\mathbf{7}\mathbf{.}\mathbf{83}\mathit{k}\mathit{m}$

$$\begin{gathered} \mathrm{θ}=ta{n}^{-1}\frac{(2.6+3.1Sin45)}{(4.0+3.1Cos45)} \\ ≈ta{n}^{-1}\frac{(4.79)}{(6.19)} \\ \mathit{θ}\mathbf{≈}\mathbf{37}\mathbf{.}\mathbf{7}\mathbf{°} \end{gathered}$$

As per mentioned all three components, Resultant and its magnitude, direction is calculated accordingly