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I have tried various methods as to answer this question using $\sin$ and $\tan$ but I cannot seem to attach my working out please send me the answers no working out needed as I just want to see where I went wrong thank you

an4s
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zee
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  • Welcome to the website. For any doubts on how to use mathematical notation please check https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – RicardoMM Mar 20 '20 at 16:11
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    Angle bwtween 2 lines from slopes arctan 2 - arctan (-1) – Narasimham Mar 20 '20 at 20:33
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    Do you know the relationship between the dot product of two vectors and the angle between them? – amd Mar 20 '20 at 21:09

2 Answers2

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$A+D+E=180°$

Now the slope of $AB$ is the same as $AD$ and it's equal to the tangent of the angle $ADE$. Instead for $AED$ we need to do $180°-AEF$ where the tangent of $AEF$ is the slope of $AE$ that is the same as $AC$.

$A+\arctan(2)+180°-\arctan(-1)=180°$

$A=\arctan(-1)-\arctan(2)$

$A=71,6°$

user289143
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  • I don't get the downvote.. – user289143 Mar 20 '20 at 16:40
  • I upvoted but you don't need a lot of the verbiage. Just take your second A= line as obvious; i.e. use the slopes as tan()... then subtract the arctan() 's of the slopes and then usual geometry. – rrogers Mar 24 '20 at 20:15
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First of all calculate the slope of both these lines by comparing with the formula of a standard equation of line as : y= mx +c , c being a constant. for line AB you will find 'm1' and for line AC , you can deduce 'm2' such that 'm1' and 'm2' being the respective slopes for the lines AB and AC. Now after deducing 'm1' and 'm2', find the angle '∆' between the lines AB and AC as: tan(∆) = (m1 - m2)/(1 + m1*m2).

Shashwat Vaibhav
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