# Calculating the gradient of a line with only the angle of the y-axis.

Check out the image, and figure out the question and give me an explanation please.

Much appreciated

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If the angle of the line with the positive $x$ axis is $\theta,$

then observe that angles of the triangle (with one angle $=15^\circ$ ) are $180^\circ-\theta,15^\circ,90^\circ.$

$\implies 180^\circ-\theta+15^\circ+90^\circ=180^\circ\implies \theta=105 ^\circ$

So, the gradient will be $$\tan \theta=\tan 105^\circ=\tan (45^\circ+60^\circ)=\frac{\tan45^\circ +\tan60^\circ}{1-\tan45^\circ \tan60^\circ}=\frac{1+\sqrt3}{1-\sqrt3}$$

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Thanks for the explanation. – Denny Jan 9 '13 at 11:06
@Denny, nice to hear that I could make the idea clear. – lab bhattacharjee Jan 9 '13 at 11:08

The gradient is $−\tan(75)$. Just calculate the angle it makes with the x-axis.

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The gradient of a line can be found if we know the angle it makes with the x-axis using the formula m=tan(θ). To find the angle it makes we merely use basic geometric reasoning, this tells us that the angle is 105 degrees. So the gradient is therefore Tan(105)

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