Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

enter image description here

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

Much appreciated

share|cite|improve this question
up vote 3 down vote accepted

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 $$\tan \theta=\tan 105^\circ=\tan (45^\circ+60^\circ)=\frac{\tan45^\circ +\tan60^\circ}{1-\tan45^\circ \tan60^\circ}=\frac{1+\sqrt3}{1-\sqrt3}$$

share|cite|improve this answer
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.

share|cite|improve this answer

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)

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.