# Given point (24,7) how do you find the distance of the point from the origin, then find the measure of the angle in standard position whose terminal side contains the point?

Mar 4, 2018

Polar coordinates of color(green)(vec(OA) => r, theta => 25, 16.26^@

#### Explanation:

Given Point $A \left(24 , 7\right)$

To find distance of A from origin $\overline{O A}$ and the measure of $\hat{A}$

Both x & y coordinates are positive and hence point A is in first quadrant.

Coordinates of origin is $O \left(0 , 0\right)$

Distance formula to calculate the distance between two points is

$r = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

Since one point (origin) has coordinates (0,0),

$r = \overline{O A} = \sqrt{x {\circ}^{2} + {y}^{2}} = \sqrt{{24}^{2} + {7}^{2}} = 25$

To find the measure of angle $\hat{\theta}$

$\tan \theta = \frac{y}{x} = \frac{7}{24}$

$\theta = \tan - 1 \left(\frac{7}{24}\right) = {16.26}^{\circ}$

Polar coordinates of color(green)(vec(OA) => r, theta => 25, 16.26^@