Math  /  Geometry

QuestionTwo points in a plane have polar coordinates (2.30 m,40.0)\left(2.30 \mathrm{~m}, 40.0^{\circ}\right) and (3.70 m,140.0)\left(3.70 \mathrm{~m}, 140.0^{\circ}\right). (a) Determine the Cartesian coordinates of these points.  ( 2.30 m,40.0 ) x= (No Response) my= (No Response) m ( 3.70 m,140.0 ) x= (No Response) my= (No Response) m\begin{array}{l} \text { ( } 2.30 \mathrm{~m}, 40.0^{\circ} \text { ) } \\ x=\text { (No Response) } \mathrm{m} \\ y=\text { (No Response) } \mathrm{m} \\ \text { ( } 3.70 \mathrm{~m}, 140.0^{\circ} \text { ) } \\ x=\text { (No Response) } \mathrm{m} \\ y=\text { (No Response) } \mathrm{m} \end{array} (b) Determine the distance between them. (No Response) m Need Help? Read It Watch it

Studdy Solution
Calculate the values: d=(4.5960)2+(0.9000)2d = \sqrt{(-4.5960)^2 + (0.9000)^2} d=21.1264+0.8100d = \sqrt{21.1264 + 0.8100} d=21.93644.6826md = \sqrt{21.9364} \approx 4.6826 \, \text{m}
The Cartesian coordinates of the points are approximately:
1. (1.7618m,1.4784m)(1.7618 \, \text{m}, 1.4784 \, \text{m})
2. (2.8342m,2.3784m)(-2.8342 \, \text{m}, 2.3784 \, \text{m})

The distance between the points is approximately: 4.6826m \boxed{4.6826 \, \text{m}}

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