Similar right-angled triangles with trigonometric ratios
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Similar right-angled triangles with trigonometric ratios
12 self-marking GCSE practice questions on Similar right-angled triangles with trigonometric ratios, written specifically for AQA, Pearson, OCR across Higher tier. Instant marking with full worked solutions on every question.
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Question 13 marksGrade 6-7
Triangle A and triangle B are two similar right-angled triangular supports, each with a right angle. In triangle A, the side adjacent to angle θ is 5 cm and the side opposite θ
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Uses an unscaled length in a second trigonometric step instead of the value found in the first step
Applied tan(θ) to triangle A's adjacent side (3 cm) instead of first scaling it by 2 to get triangle B's adjacent side (6 cm) - the scale factor step was skipped.
Uses the reciprocal trig ratio in the second of two connected right-angled triangles
Divided by tan(θ) instead of multiplying when finding the opposite side in triangle B - since opposite =adjacent×tan(θ)
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is 9 cm. Triangle
B
is similar to triangle
A
with a linear scale factor of 3. Work out the size of angle
θ
(correct to 3 significant figures), and the length of the side in triangle
B
that corresponds to the 5 cm side in triangle
A
.
Show the worked solution
tan(θ)=adjacentopposite=59, so θ=tan−1(59)=60.9° (3 s.f.) M1A1
The corresponding side in triangle B is scaled by the linear scale factor 3: 5×3=15 cm A2
Note: the diagram also shows the opposite side in triangle B as 27 cm, found the same way: 9×3=27 cm.
Uses the squared (area) scale factor where the linear scale factor was needed
Squared the linear scale factor (as if finding an area ratio) instead of applying it once to the length - for a length in a similar figure, the scale factor is applied only once, not squared.