Topic: Trigonometric Ratios and Applications

The distress call crackled: “Injured hiker on cliff face. Need exact location.”

Rescue pilot Chen had two observation points 500 meters apart. From point A, the angle of elevation to the hiker was 35°. From point B, it was 48°.

She quickly sketched triangles. Using tan(35°) = h/x and tan(48°) = h/(500-x), she set up simultaneous equations.

“Height is 412 meters, horizontal distance 588 meters from base camp,” she radioed.

The helicopter crew found the hiker within minutes. As they lifted off, the young hiker asked, “How did you find me so fast?”

Chen smiled. “Trigonometry. These ratios have been helping navigators and rescuers for centuries. The angles told us exactly where you were.”

The Math Behind It: Trigonometry transforms angles into distances. Surveyors, pilots, architects, and rescue teams use these ratios daily. Three measurements (two angles, one distance) can determine any position—a principle called triangulation.