Opposite and adjacent depend on the chosen angle. The hypotenuse does not: it is always opposite the right angle. Mark the angle first, name the sides second, and only then choose a trigonometric ratio.
Curriculum checked 2 October 2026 · original practice for selected skills.
You will need: Pythagoras, fractions and square roots.
Attempt each task before opening a hint. If you need help, reveal the first hint, then the setup, then compare your written steps with the solution. Finish with the retests without referring back.
For an acute angle θ in a right triangle, sin θ=opposite/hypotenuse, cos θ=adjacent/hypotenuse and tan θ=opposite/adjacent.
The identity sin²θ+cos²θ=1 involves squares. It does not say sin θ+cos θ=1.
Height-and-distance models need a clear right triangle. If eye level is above ground, include that height when the question asks for total object height.
The side of length 5 is opposite θ.
Use 13 as the hypotenuse and 12 as the adjacent side.
sin θ=5/13 and cos θ=12/13.
tan θ=5/12; check (5/13)²+(12/13)²=1.
Answer: 5/13, 12/13 and 5/12
Before moving on: can you explain why your method works, as well as give the answer?
Write a method as well as an answer. The tasks change the reasoning, not just the numbers.
Use the squared identity or a 3–4–5 triangle.
cos²θ=1−9/25.
cos²θ=16/25.
The acute-angle cosine is positive.
Answer: 4/5
Before moving on: can you explain why your method works, as well as give the answer?
Both trigonometric values are 1/2.
Substitute before adding.
2 × 1/2=1.
1+1/2=3/2.
Answer: 3/2
Before moving on: can you explain why your method works, as well as give the answer?
Height is opposite and ground distance adjacent.
tan45°=h/10=1.
The hypotenuse is unnecessary.
h=10 m.
Answer: 10 m
Before moving on: can you explain why your method works, as well as give the answer?
A tempting claim: “The side that looks vertical is always opposite.”
Opposite is defined relative to the chosen angle, not the orientation of the drawing.
These changed questions test whether you can reconstruct the method. If you use a hint, record where you got stuck and retry later. Completing this small set does not establish full chapter mastery.
Find the hypotenuse first.
√(8²+15²)=17.
The square sum is 289.
sin θ=8/17 and tan θ=8/15.
Answer: 8/17 and 8/15
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
Use tangent and keep the root exact.
h=12/√3.
tan30°=h/12.
12/√3=4√3.
Answer: 4√3 m
Could you solve this without the earlier example? If not, revisit the first line where you got stuck.
If a retest exposed the same error, rewrite the first incorrect step and explain its correction aloud. If both were independent, return to a mixed exercise or a missed paper question. A parent can ask what changed in the method rather than only asking for the answer.
Keep fractions and square roots exact unless a question asks for a decimal approximation. Rounding early can make later steps less accurate.
Yes. Use the two print buttons above. The question sheet leaves working space and hides solutions; the worked-solutions option includes the solution steps. Your browser can save either view as a PDF.
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