Trigonometry question: For the point A (5; 0) and B (7;3) calculate the angle between AB and the x-axis.The answer given in the book is as follows:56.3 degrees

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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Sorry but I'm only permitted to answer your first question. Please post each of the others as individual questions and then they will be answered promptly.

A is at point (5;0) which means it is on the x-axis. B is at (7;3).

Draw a triangle along a set of axes marking A  at (5;0). Then at (7;0) on the same axis plot a point - call it C if you like. From C  draw a vertical line up until you reach (7;3) and mark point B. Now join A and B. Your 90 degree angle is at point C.

The distance from A to C is 2 units (7 - 5) and the distance from C to B is 3 units (from x-axis to 3).

Therefore tan theta = 3/2.

Use the shift key or 2nd function key on your calculator and you will get

tan theta = 56,3 degrees.