Reach for the Star

Trigonometry in right triangles · Optional extension

L039 · Allow 10–15 minutes for learners ready to move on. Answers are available after an attempt.

Stretch

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

Reveal a worked check after attempting

8 tan 35°≈5.60 cm.

Deep challenge

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

Reveal a worked check after attempting

Opposites are 5 cm and 12.5 cm, ratio 2:5, matching the hypotenuse ratio.

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.