Applications of Trigonometric Ratios: Finding Lengths

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Learning objective overview

Master Teaching Guide coverage for this objective.

CorbettMaths on using trigonometry to solve for unknown sidesQuestions PDF · Answers
Beta: Exercise 22.01, pg 422
Beta: Exercise 22.13, pg 441
Beta: Exercise 22.14, pg 442
Beta: Parallel Skills Exercise 22C, pgs 442 & 443
Beta: Application: Ex 23.03, pgs 448 & 449

Label the hypotenuse, adjacent, and opposite sides of a right-angled triangle relative to a given angle.
Choose and apply the correct trigonometric ratio (sine, cosine, or tangent) to find a missing side length given an angle and one other side length.
Find a missing side length from a labelled diagram giving an angle and one side length of a right-angled triangle.
Round a calculated length to one or two decimal places, as instructed.
Solve a real-world worded problem (such as a ladder, ramp, kite string, tree shadow, or building) by finding an unknown height, distance, or length using a given angle.
Find two unknown side lengths of the same right-angled triangle from a single given angle and side length.
Solve a multi-step problem that combines finding a length with finding an angle, or that involves the triangle's dimensions changing (for example, moving the observation or anchor point) and recalculating.

This application objective follows Trigonometric Ratios: Finding a Side and uses the same SOH CAH TOA calculations inside real-world word problems.
Require students to translate contexts such as ladders, ramps, shadows, buildings, wires, elevation, and depression into a labelled right-angled triangle before calculating.
Emphasise what each side represents, correct units, sensible rounding, and a reasonableness check against the physical situation.
Keep direct, already-drawn triangle practice in the core finding-a-side objective; the distinctive demand here is modelling and interpreting the context.