Overview

Integrated Math II

35. CC.HSG.SRT.C.8

35.4 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

Drawing diagrams from written descriptions of angle situations

Finding distances using angles of elevation and depression

Solving building height problems with multiple triangles

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.

Before You Start — Make Sure You Can:

Use sine ratio to calculate angles and sides (Sin = \( \frac{o}{h}\) )Use cosine ratio to calculate angles and sides (Cos = \( \frac{a}{h}\) )Use tangent ratio to calculate angles and sides (Tan = \( \frac{o}{a}\) )Combination of SohCahToa questions

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

OH Curriculum Aligned