1. Trigonometry – Introduction – Worksheet A
This resource includes three worksheets designed to aid the
discovery of Sine, Cosine & Tangent trigonometric ratios.
Each worksheet is in a variety of sizes.

2. Printing To print handouts from slides -
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3. 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = Discovering Trigonometry B5
Measure each triangle
and complete the table. B4 B3
Triangle 1 B2 B1
15° A C1 C2 C3 C4 C5
We want to find the ratio of the
opposite side to the hypotenuse.
Labelling a
right-angled
triangle
Hypotenuse
Opposite
Side
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Adjacent
Side

4. SINE Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the opposite side
to the hypotenuse of a triangle?
80°
60° A
SINE C1 C2 C3 C1 C2 C3 C4 C5

5. 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = Discovering Trigonometry B5
Measure each triangle
and complete the table. B4 B3
Triangle 1 B2 B1
15° A C1 C2 C3 C4 C5
We want to find the ratio of the
adjacent side to the hypotenuse.
Labelling a
right-angled
triangle
Hypotenuse
Opposite
Side
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Adjacent
Side

6. COSINE Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the adjacent side
to the hypotenuse of a triangle?
80°
60° A
COSINE C1 C2 C3 C1 C2 C3 C4 C5

7. 𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = Discovering Trigonometry B5 Measure each triangle
and complete the table. B4 B3
Triangle 1 B2 B1
15° A C1 C2 C3 C4 C5
We want to find the ratio of the
opposite side to the adjacent side.
Labelling a
right-angled
triangle
Hypotenuse
Opposite
Side
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
Adjacent
Side

8. TANGENT Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the opposite side
to the adjacent side of a triangle?
80°
60° A
TANGENT C1 C2 C3 C1 C2 C3 C4 C5

9. 0.26 0.5 0.98 0.87 SINE Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.26
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.5 B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.98
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.87 B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the opposite side
to the hypotenuse of a triangle?
80°
60° A
SINE C1 C2 C3 C1 C2 C3 C4 C5

10. 0.97 0.87 0.17 0.5 COSINE Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.97
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.87 B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.17
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
0.5 B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the adjacent side
to the hypotenuse of a triangle?
80°
60° A
COSINE C1 C2 C3 C1 C2 C3 C4 C5

11. 0.27 0.58 5.67 1.73 TANGENT Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
0.27
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
0.58 B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
5.67
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
1.73 B3
Opposite
Side
Adjacent
Hypotenuse B1 B2 B1
Triangle 4
What comments can you make
about the ratio of
the opposite side
to the adjacent side of a triangle?
80°
60° A
TANGENT C1 C2 C3 C1 C2 C3 C4 C5

12. SINE Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐵1𝐶1 𝐴𝐵1 = =
𝐵2𝐶2 𝐴𝐵2 =
𝐵3𝐶3 𝐴𝐵3 =
𝐵4𝐶4 𝐴𝐵4 =
𝐵5𝐶5 𝐴𝐵5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the opposite side
to the hypotenuse of a triangle?
80°
60° A
SINE C1 C2 C3 C1 C2 C3 C4 C5

15. COSINE Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 =
Triangle °
𝐴𝐶1 𝐴𝐵1 = =
𝐴𝐶2 𝐴𝐵2 =
𝐴𝐶3 𝐴𝐵3 =
𝐴𝐶4 𝐴𝐵4 =
𝐴𝐶5 𝐴𝐵5 =
Mean =
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the adjacent side
to the hypotenuse of a triangle?
80°
60° A
COSINE C1 C2 C3 C1 C2 C3 C4 C5

18. TANGENT Discovering Trigonometry B5
Give your answers to 2 decimal places.
Measure each of the four triangles
and complete the tables opposite. B4
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = B3 B2
Triangle 1 B1
15° A C1 C2 C3 C4 C5 B3 B4 B5 B3
Triangle 2 B2
Triangle 3 B1 B2 B4
30° C1 C2 C3 C4
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 =
Triangle °
𝐵1𝐶1 𝐴𝐶1 = =
𝐵2𝐶2 𝐴𝐶2 =
𝐵3𝐶3 𝐴𝐶3 =
𝐵4𝐶4 𝐴𝐶4 =
𝐵5𝐶5 𝐴𝐶5 =
Mean =
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 = B3
Opposite
Side
Adjacent B1
Hypotenuse B2 B1
Triangle 4
What comments can you make
about the ratio of
the opposite side
to the adjacent side of a triangle?
80°
60° A
TANGENT C1 C2 C3 C1 C2 C3 C4 C5

21. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
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