Points locked

Trigonometry in right triangles

L039 · GCSE Mathematics 1MA1 · 60 minutes

Objective: Select sine, cosine or tangent to find a missing side or angle in a right-angled triangle and justify the chosen ratio.

Connect & Check · 5 min

Baseline

In a right triangle, which side is always the hypotenuse?

Relative to an angle θ, explain how to identify the opposite and adjacent sides.

Share · 5 min

Route choice

Present · 12 min

Adjacent = 8 cm and θ = 35°. Find the opposite side.

Apply · 25 min

Supported → independent

Angle θ=30°, hypotenuse=10 cm. Find the opposite side.

Adjacent=12 cm, θ=28°. Find the hypotenuse to 1 d.p.

A ladder 5.5 m long makes an angle of 68° with the ground. How high up the wall does it reach? Give 2 d.p.

Recall & Review · 8 min

A right triangle has opposite side 6 cm and adjacent side 11 cm relative to θ. Find θ to 1 d.p. and state the ratio used.

Points and self-check

Complete every stage to unlock.

Recall & Review: feedback and extension integration

Lesson L039: Trigonometry in right triangles

Objective: Select sine, cosine or tangent to find a right-triangle side or angle.

60-minute structure: 0-7 Connect & Check; 7-14 Share; 14-25 Present/model; 25-44 Apply route choice/practice; 44-52 independent exam-style check; 52-60 Recall & Review, WWW/EBI and next step.

What Went Well (WWW)

I selected the correct geometric fact, theorem, formula or transformation and used a clear diagram with appropriate labels and units.

Even Better If (EBI)

I will name the fact or theorem, show the substitution or construction step and check whether the size, direction and units of the result are reasonable.

Stretch and deep challenge

Stretch: A right triangle has adjacent side 8 cm and an angle of 35°. Find the opposite side to 2 d.p.

Deep challenge: Two right triangles share angle 30° but have hypotenuses 10 cm and 25 cm. Compare their opposite sides.