Trigonometry Missing Sides & Angles Practice | Right Angled Triangles Worksheet

A comprehensive right-angled triangles maths worksheet featuring multi-part questions with fully worked step-by-step solutions. Covers SOH CAH TOA trigonometric ratios, Pythagoras’ Theorem, and exact values for special 30-60-90 and 45-45-90 triangles. Perfect for KS4 revision, homework, cover lessons, and GCSE preparation.

This Trigonometry Missing Sides & Angles Practice Worksheet provides structured, comprehensive practice for students navigating right triangle geometric properties. By combining basic trigonometric functions with multi-step coordinate problems and exact value applications, this resource ensures deep conceptual understanding and arithmetic fluency.
Every single problem in this pack includes a fully worked-out, step-by-step solution sheet—giving your students a clear roadmap for self-correction, saving you valuable marking time, and serving as a perfect zero-prep packet to leave for a cover lesson!

What Is Included in This Pack?
This high-utility maths worksheet includes structured problems targeting three core algebraic and geometric milestones:
• SOH CAH TOA Trigonometric Ratios: Calculation practice for finding unknown side lengths and missing acute angles using sine, cosine, and tangent operations.
• Pythagoras’ Theorem Integration: Scaffolded problems requiring students to solve for missing side values before applying inverse trigonometric ratios (e.g., using Pythagoras to find a hypotenuse, then calculating the acute angle).
• Special Triangles & Exact Values: Advanced multi-step problems calculating exact side lengths in radical/surd form for 45-45-90 and 30-60-90 triangles (e.g., leaving answers as simplified surds like 4√2 or 2√3).

Key Features & Benefits
• Fully Worked Solutions: No simple final answers or hidden steps! Students can see every side manipulation, division step, and surd reduction used to reach the final answer.
• Zero Prep Required: Just print and copy! Excellent for weekly homework, independent classwork, or structured revision booklets.
• Scaffolded Learning: Intentionally designed to progress from standard decimal rounding tasks to complex, exact-value algebraic fractions.
• UK Classroom Ready: Fully aligned to UK maths curriculum language, utilising metric measurements (cm) and standard geometric layouts.

Curriculum Alignment
• Key Stages: KS4 (Years 10–11)
• GCSE Maths Assessment Objectives (Foundation & Higher Tier Focus):
o G20: Know the formulae for Pythagoras’ Theorem and the trigonometric ratios; apply them to find angles and lengths in right-angled triangles in two dimensions.
o G21: Know the exact values of sinθ and cosθ for θ = 0°, 30°, 45°, 60°, 90°; know the exact value of tanθ for θ = 0°, 30°, 45°, 60°.