Trigonometric Applications and Bearings

Trigonometric Applications and Bearings

Applications turn a diagram into a trigonometric model. Bearings are measured clockwise from north and written as three digits. Decide whether a triangle is right-angled or general, label known lengths/angles, and calculate one relationship at a time. Finish by interpreting the answer with a unit and a sensible rounding level.

Worked reasoning

From a point, a boat is 80 km on a bearing of $060^\circ$. The north component is $80\cos60^\circ=40$ km and east component is $80\sin60^\circ\approx69.3$ km.

Exam method

1. Draw north lines and label bearing clockwise. 2. Split/generalise the triangle. 3. Choose a rule, calculate, and state the contextual answer.

Context can check the calculation

After finding a distance, bearing or height, ask whether the direction and size fit the sketch. A north-east bearing should produce positive north and east components; a ladder’s vertical height must be shorter than its length. Label every side with units before choosing a trig ratio. In multi-stage problems, mark the answer from one triangle onto the next one. This keeps the geometric model connected to the story and avoids using a correct formula on the wrong angle.

One-minute retrieval: Trigonometric Applications and Bearings

Close the worked solution. From memory, state its central rule, name one condition that makes it valid, and reconstruct one check that would catch a typical exam error.