In everyday practice - mainly to understand what he is doing - how aiming occurs, focusing in stereotaxic surgery, how a cyber knife irradiates exactly the area that the surgeon wants, without damaging healthy tissue.
And the direct application of the knowledge of trigonometry is the lot of developers and doctors engaged in science.
How will you find the projection of the Shipo triangle during an operation for mastoiditis? Or determine the Garland and Rauchfus-Grokko triangles with exudative pleurisy from X-rays? Or Kahlo's triangle for cholecystectomy?
In fact, knowing trigonometry directly is hardly useful to you. Another thing is that geometry and algebra develop in a person logical thinking, without which it is difficult to imagine clinical thinking.
UPD: I still found an example for you - the technique of perirenal blockade: "After the usual anesthesia of the skin, a long (10-12 cm) needle is injected at the apex of the angle formed by the XII edge and the outer edge of the muscle straightening the spine, perpendicular to the body surface. Continuously injecting 0.25% novocaine solution, the needle is advanced until its end penetrates through the retrenal fascia into the perirenal cellular tissue space. fiber resistance to the entry of novocaine into the needle disappears.In the absence of blood and urine in the syringe, when the piston is pulled, 60-80 ml of a 0.25% solution of novocaine warmed to body temperature is injected into the perineal tissue. "
UPD2: did not notice, that the question is about a neurosurgeon. In this case, knowledge of trigonometry will allow you to determine the position of the sinuses of the brain according to the Cronlein-Bryusova projection scheme: "The following lines are drawn on the scalp: 1) the lower horizontal (main) line follows through the lower edge of the orbit and the upper edge of the external auditory canal; 2) the upper horizontal line runs parallel to the first and follows through the upper edge of the orbit; 3) the midline of the skull follows the sagittal suture from the bridge of the nose to the external occipital protuberance; 4) the anterior vertical line passes through the middle of the zygomatic arch; 5) the middle vertical line goes through the middle of the articular head the lower jaw; 6) the posterior vertical line goes through the posterior point of the base of the mastoid process; 7) the line connecting the intersection of the upper horizontal with the first vertical and the midline with the posterior vertical; 8) the line that forms the bisector of the angle formed by the previous line and the upper horizontal; 9) the third horizontal line (Bryusova), with leading parallel to the upper contour through the intersection of the trailing vertical with the bisector. "