Introduction to Trigonometry - Go Teach Maths: Handcrafted - Free Printable

Let’s solve each part of the worksheet step by step, using basic trigonometry (SOH-CAH-TOA).

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## Part 1: Calculate the unknown side in each of the following

We are given trig equations and need to solve for the unknown variable.

> Remember:
> - sin(θ) = opposite / hypotenuse
> - cos(θ) = adjacent / hypotenuse
> - tan(θ) = opposite / adjacent

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a) sin 20° = a / 15

→ Multiply both sides by 15:
a = 15 × sin 20°
Using calculator: sin 20° ≈ 0.3420
→ a ≈ 15 × 0.3420 = 5.13 m

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b) cos 37° = b / 30

→ b = 30 × cos 37°
cos 37° ≈ 0.7986
→ b ≈ 30 × 0.7986 = 23.96 m

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c) tan 64° = c / 5

→ c = 5 × tan 64°
tan 64° ≈ 2.0503
→ c ≈ 5 × 2.0503 = 10.25 m

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d) sin 52° = d / 32

→ d = 32 × sin 52°
sin 52° ≈ 0.7880
→ d ≈ 32 × 0.7880 = 25.22 m

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e) cos 10° = e / 18

→ e = 18 × cos 10°
cos 10° ≈ 0.9848
→ e ≈ 18 × 0.9848 = 17.73 m

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f) tan 25° = f / 22

→ f = 22 × tan 25°
tan 25° ≈ 0.4663
→ f ≈ 22 × 0.4663 = 10.26 m

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✔ Answers for Part 1:
a) 5.13 m
b) 23.96 m
c) 10.25 m
d) 25.22 m
e) 17.73 m
f) 10.26 m

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## Part 2: Calculate the lengths of the lettered sides

Each triangle has one known side and one known angle. We’ll use SOH-CAH-TOA to find the unknown side.

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Triangle 1 (top left):

Right triangle, angle = 60°, hypotenuse = 12, find a (adjacent to 60°)

→ Use cos (adjacent/hypotenuse)
cos 60° = a / 12
→ a = 12 × cos 60° = 12 × 0.5 = 6 m

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Triangle 2 (top middle):

Right triangle, angle = 45°, opposite side = 8, find c (hypotenuse)

→ Use sin (opposite/hypotenuse)
sin 45° = 8 / c
→ c = 8 / sin 45° = 8 / (√2/2) = 8 × 2/√2 = 16/√2 = 8√2 ≈ 11.31 m

*(Note: sin 45° = √2/2 ≈ 0.7071 → c ≈ 8 / 0.7071 ≈ 11.31)*

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Triangle 3 (top right):

Right triangle, angle = 25°, hypotenuse = 15, find e (adjacent to 25°)

→ Use cos
cos 25° = e / 15
→ e = 15 × cos 25° ≈ 15 × 0.9063 = 13.59 m

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Triangle 4 (bottom left):

Right triangle, angle = 35°, adjacent side = 24, find b (opposite to 35°)

→ Use tan
tan 35° = b / 24
→ b = 24 × tan 35° ≈ 24 × 0.7002 = 16.80 m

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Triangle 5 (bottom middle):

Right triangle, angle = 26°, hypotenuse = 15, find d (adjacent to 26°)

→ Use cos
cos 26° = d / 15
→ d = 15 × cos 26° ≈ 15 × 0.8988 = 13.48 m

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Triangle 6 (bottom right):

Right triangle, angle = 70°, hypotenuse = 17, find f (adjacent to 70°)

→ Use cos
cos 70° = f / 17
→ f = 17 × cos 70° ≈ 17 × 0.3420 = 5.81 m

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✔ Answers for Part 2:
a) 6 m
c) 11.31 m
e) 13.59 m
b) 16.80 m
d) 13.48 m
f) 5.81 m

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## Part 3: Flagpole problem

> A flagpole is held upright by 30m long wires to the ground. The wires make an angle of 25° to the ground. How high is the flagpole?

This is a right triangle problem:

- The wire is the hypotenuse = 30m
- The angle with the ground = 25°
- The height of the flagpole is the opposite side to the 25° angle

→ Use sin (opposite/hypotenuse)
sin 25° = height / 30
→ height = 30 × sin 25° ≈ 30 × 0.4226 = 12.68 m

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✔ Answer for Part 3: The flagpole is approximately 12.68 meters high.

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## ✔ Final Summary of All Answers:

Part 1:

a) 5.13 m
b) 23.96 m
c) 10.25 m
d) 25.22 m
e) 17.73 m
f) 10.26 m

Part 2:

a) 6 m
c) 11.31 m
e) 13.59 m
b) 16.80 m
d) 13.48 m
f) 5.81 m

Part 3:

12.68 m

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Let me know if you’d like diagrams or step-by-step calculator instructions!