What you’ll learn
Model real situations using trig.
Key idea
The ladder is opposite the right angle; the vertical reach is opposite the ground angle.
Vertical reach is opposite the ground angle and the sloping ladder is the hypotenuse.
Worked example
Enter the exact value or ordered values in the format requested below.
A 13-meter ladder makes a 60-degree angle with level ground against a vertical wall. Its vertical reach is h. Write the unsolved trig equation using h and the ladder length.
- The ladder length 13 is the hypotenuse and h is opposite the ground angle.
- Sine is opposite/hypotenuse, so the unsolved model is sin60°=h/13.
Answer: sin60°=h/13
Quick Check
Choose which candidate representation satisfies the requirements of 'Model real situations using trig' and justify the choice.
A 26-meter ladder makes a 30-degree angle with level ground against a vertical wall. Its vertical reach is h. A diagram supplies candidate models sin30°=h/26, cos30°=h/26, tan30°=26/h. Select and justify the valid model.