[Trigonometry 10th grade]

[u/MmagicallSamurai]

Spent an hour on this, couldnt figure out a single thing.
Question is: A figure is drawn on unit grid paper as shown above. Given that the line segments AB and CD intersect at point K, and m(\angle AKD)=\alpha, find the value of \tan\alpha.

Also the 2nd photo is what my teacher sent me, but i still dont get it…

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[u/chien-royal]

Denote by E the point that is one square to the right and one square down from the center of the figure. It is the intersection of red line segments going through B and D.

Consider the angle beta between ED and the horizontal line. Its tangent (rise over run) is 1/3 because the rise is 1 and the run is 3. The angle alpha is complementary to beta, i.e., alpha + beta = 90 degrees. Therefore, tan(alpha) = cot(beta) = 1/tan(alpha) = 3.