Final Answer:
The worksheet requires measuring angles and side lengths of six right-angled triangles (a–f), labeling opposite/adjacent sides relative to the marked angle, computing three trigonometric ratios (sin = Opposite/Hypotenuse, cos = Adjacent/Hypotenuse, tan = Opposite/Adjacent), and recording all values in the table. Then answer questions 5 and 6 conceptually:
5. No — the ratios
Opposite/Hypotenuse and
Adjacent/Hypotenuse cannot be greater than 1, because in a right triangle, the hypotenuse is always the longest side, so both opposite and adjacent are shorter than or equal to the hypotenuse.
6. The ratio
Opposite/Adjacent (tangent) can be greater than 1 — there’s no upper limit. As the marked angle gets closer to 90°, the opposite side becomes much longer than the adjacent side, so the ratio grows without bound (e.g., for a 75° angle, tan ≈ 3.73). So the greatest value is *unlimited* (it can be as large as you want, depending on the angle).
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Parent Tip: Review the logic above to help your child master the concept of ratios triangles worksheet.
