Question

Two points in a plane have polar coordinates ( 2.50 m, 30 degrees) and (3.80m, 120 degrees0
Determine the cartesian coordinates and the distance between them.

Answer 1

Answer on Question #79897 - Math - Geometry

Two points in a plane have polar coordinates $(2.50\ \mathrm{m},\ 30.0{}^{\circ})$ and $(3.80\ \mathrm{m},\ 120.0{}^{\circ})$. Determine (a) the Cartesian coordinates of these points and (b) the distance between them.

(a) $x = r \cos \theta \quad y = r \sin \theta$

$$x_1 = (2.50\ \mathrm{m}) \cos 30{}^\circ \quad y_1 = (2.50\ \mathrm{m}) \sin 30{}^\circ$$ $$(x_1, y_1) = \boxed{(2.17, 1.25)\ \mathrm{m}}$$ $$x_2 = (3.80\ \mathrm{m}) \cos 120{}^\circ \quad y_2 = (3.80\ \mathrm{m}) \sin 120{}^\circ$$ $$(x_2, y_2) = \boxed{(-1.90, 3.29)\ \mathrm{m}}$$

(b) $d = \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{16.6 + 4.16} = \boxed{4.55\ \mathrm{m}}$

where $\Delta x = x - x$, $\Delta y = y - y$.

cos $30{}^\circ \approx 0.866$

sin $30{}^\circ = 0.5$

cos $120{}^\circ = -0.5$

sin $120{}^\circ = 0.866$

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