# How do you write in simplest radical form the coordinates of point A if A is on the terminal side of angle in standard position whose degree measure is theta: OA=15, theta=135^circ?

Nov 17, 2017

The coordinates are $\left(\frac{15}{\sqrt{2}} , \frac{15}{\sqrt{2}}\right)$

#### Explanation:

Start by making a reference triangle for your angle.

The inner angle of the right triangle is $180 - 135 = 45$ degrees. The side opposite the $45$ degree angle is the $y$ coordinate, and the side adjacent to the $45$ degree angle is the $x$ coordinate.

The properties of a $45 - 45 - 90$ right triangle are

So the hypotenuse is $15 = y \sqrt{2}$. We can solve this by dividing both sides by $\sqrt{2}$.

$x = \frac{15}{\sqrt{2}}$ and $y = \frac{15}{\sqrt{2}}$.

Thus, the coordinates are $\left(\frac{15}{\sqrt{2}} , \frac{15}{\sqrt{2}}\right)$