Why?

Why?
It can be an infuriating question. Especially, when you perceive the person asking, to be questioning your authority, and not merely on a quest for knowledge. (You spoiled, rotten, little smart aleck. I'll show YOU why). Don't rush to a snap decision. Find the motivation for the question. Ask "WHY? What?" You have not turned the tide. But, you are going to learn something about the person who started it. And be be preared if another question is fired back in chain-gun staccato.
If the new question "Why do I need to know Trigonometry?" Is fired at you. Be prepared to respond. But you need to know what interests your inquisitor. Or you will get caught in a Quagmire of Vietnam proportions. A teacher is not an entertainer. Humor is a viable teaching tool. But it is not required. And when someone asks you a question. Like it, or not. They have placed you in the teacher position.
Okay? Let's proceed...
"You need trig, so you can figure the height of the flag pole in front of the school, with out climbing it."
"But, the flag pole has a plaque with the height on it." (Don't be tempted to say "What if it isn't accurate?" Quagmire alert).
Change the subject to something that may appeal to your student and the others in attendance. Give an interesting fact of how a real-life person used trig to solve a real-life problem. Of course this tool is not available to the specialized teacher. A general practitioner is more capable of diagnosing the flu, than a cardiac-surgeon. But, before you can mention the name "Eratosthenes". If you think George Washington is the dollar bill dude. Or The proper way to address Jeanne d'Arc is "Hello miss 'Of Arc". You may want to find another profession.
You will have had to know the historical background of trigonometry. 5 centuries before Christ, and 1900 years before Columbus, a man, a brilliant man, a man so brilliant that his Greek contemporaries nick-named him BETA, because his knowledge was second only to god, whio was named Eratosthenes lived. And he used trigonometry to prove the earth was round and exactly how big it was. (Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city of Syene (the modern day Aswan) on the Tropic of Cancer, the sun would appear at the zenith, directly overhead. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation of the Sun would be 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. If we assume that Eratosthenes used the "Egyptian stadium"of about 157.5 m, his measurement turns out to be 39,690 km, an error of less than 1%.). He used trigonometry to find the third side of a cosmic triangle.
Maybe Columbus could have saved himself grief if he had this knowledge before setting sail. But what if your student doesn't give a fury little rats rear-end about history? How about ballistics? or rockets? Every kid loves bullets and bombs. Well, you need trig to solve for aim point when trying to hit a target in motion and for wind deflection when your target is stationary. It wasn't until Napoleon taught the world that bullets followed an arc in flight, and did not fly in straight lines.That we learned about the ballistic curve. To hit a target at distance. You must aim high.
Of course there still exist one more possibility. Your authority is actually being challenged.
KW