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Mathematics at Work 11
Geometry
3. Solve problems involving two and three right triangles
3.6 Other word problems relating angles in trigonometry
Angle Word Problems in Trigonometry
Real-world objects like a kite string or ramp form a right triangle you can solve with sine, cosine, or tangent.
What You'll Learn
Identify the hypotenuse (often a string, rope, or sightline), the given angle, and the unknown side.
Use sine (opposite/hypotenuse) to find a height.
Use cosine (adjacent/hypotenuse) to find a horizontal distance.
The setup is the same pattern as ladder and guy wire problems.
Sketching the triangle first turns a word problem into a short calculation.
What You'll Practice
1
Drawing diagrams from written descriptions of angle situations
2
Finding distances using angles of elevation and depression
3
Solving building height problems with multiple triangles
4
Calculating diagonal lengths in three-dimensional shapes using Pythagoras
Why This Matters
These problem-solving skills prepare you for fields like surveying, architecture, engineering, and navigation where angles and distances must be calculated from real-world observations. Mastering word problems builds critical thinking and the ability to translate practical situations into mathematical models.
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Angle of Elevation
Angle of Depression
Right Triangles
Trigonometric Ratios
Pythagorean Theorem
Word Problems
Problem Solving
NS Curriculum Aligned