(Solved): The relation linking the true dip angle \( \delta \), and the apparent dip angle \( \alpha \), and ...

The relation linking the true dip angle \( \delta \), and the apparent dip angle \( \alpha \), and the angle between the strike direction and the apparent dip direction \( \beta \) involve a series of right triangles. Because of the right triangles, we can use simple trigonometric identities to show that the relation between the angles is \[ \tan \alpha=\tan \delta \sin \beta \] 1) Using the line lengths given below (like \( O B \), or \( O A \), or \( O X \), etc) what is ? \( \tan \alpha=\quad \tan \delta=\quad \sin \beta= \) Hint: have you heard of SOHCAHTOA? 2) Now substitute these into the equation above, simply if lines of equal length are both in the denominator and the numerator (i.e, they cross out). 3) If both sides of the rewritten equation are equal, then you have shown that the trig equation above is true.