Trig Review Worksheet - Free Printable

Let’s solve each triangle one by one. We’ll use trigonometry ratios: sine, cosine, and tangent. Remember:

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

We’ll pick the right ratio based on which sides we know and which side we’re trying to find.

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a)
Right triangle with angle 39°, hypotenuse = 8 cm, missing side is adjacent to 39°.

→ Use cos(39°) = adjacent / 8

So, adjacent = 8 × cos(39°)

Calculate:
cos(39°) ≈ 0.7771
8 × 0.7771 ≈ 6.2168 → 6.2 cm (to 1 decimal place)

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b)
Right triangle with angle 49°, hypotenuse = 10 cm, missing side is opposite to 49°.

→ Use sin(49°) = opposite / 10

opposite = 10 × sin(49°)

sin(49°) ≈ 0.7547
10 × 0.7547 ≈ 7.547 → 7.5 cm

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c)
Right triangle with angle 57°, adjacent side = 6 cm, missing side is hypotenuse.

→ Use cos(57°) = 6 / hypotenuse

So, hypotenuse = 6 / cos(57°)

cos(57°) ≈ 0.5446
6 ÷ 0.5446 ≈ 11.017 → 11.0 cm

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d)
Right triangle with angle 35°, adjacent side = 8 cm, missing side is opposite.

→ Use tan(35°) = opposite / 8

opposite = 8 × tan(35°)

tan(35°) ≈ 0.7002
8 × 0.7002 ≈ 5.6016 → 5.6 cm

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e)
Right triangle with angle 42°, opposite side = 5 cm, missing side is hypotenuse.

→ Use sin(42°) = 5 / hypotenuse

hypotenuse = 5 / sin(42°)

sin(42°) ≈ 0.6691
5 ÷ 0.6691 ≈ 7.472 → 7.5 cm

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f)
Right triangle with angle 28°, adjacent side = 6 cm, missing side is hypotenuse.

→ Use cos(28°) = 6 / hypotenuse

hypotenuse = 6 / cos(28°)

cos(28°) ≈ 0.8829
6 ÷ 0.8829 ≈ 6.795 → 6.8 cm

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Now let’s list all answers:

a) 6.2 cm
b) 7.5 cm
c) 11.0 cm
d) 5.6 cm
e) 7.5 cm
f) 6.8 cm

Note: b and e both give 7.5 — that’s okay, different triangles can have same side length.

Final Answer:
a) 6.2
b) 7.5
c) 11.0
d) 5.6
e) 7.5
f) 6.8