Question

What is the angle between the kayakers? Round your answer to the nearest degree.

Answer 1

The given forces are

`F_1=\langle190,160\rangle,F_2=\langle128,-121\rangle`

To find the angle, the formula for angle between two vectors will be used

`\cos \theta=(a.b)/(|a\mleft\Vert b\mright|)`

Using the given forces, it follows

`\cos \theta=\frac{190(128)+160(-121)}{(\sqrt[]{190^2+160^2})(\sqrt[]{128^2+(-121)^2})}`

Simplify the equation

`\cos \theta=\frac{24320-19360}{(\sqrt[]{36100+25600})(\sqrt[]{16384+14641})}`

Simplify further

`\begin{gathered} \cos \theta=(4960)/(248.40*176.1) \\ \cos \theta=0.1134 \end{gathered}`

Find the value of theta

`\begin{gathered} \theta=\cos ^(-1)(0.1134)_{} \\ \theta=83^(\circ) \end{gathered}`

Therefore, the required answer is

`\theta=83^(\circ)`