Primary Trig Ratios Worksheets | Sine, Cosine, Tangent - Free Printable

Let’s solve each problem one by one. We’ll use the basic trigonometric ratios:

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

We’ll identify the sides relative to the angle given, then plug into the correct ratio.

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1) tan B

In triangle ABC, angle B is at the bottom left.

Side opposite to angle B = AC = 28
Side adjacent to angle B = BC = 45
(Hypotenuse AB = 53 — we don’t need it for tangent)

So,
tan B = opposite / adjacent = 28 / 45

That’s already simplified (28 and 45 share no common factors).

→ Answer: 28/45

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2) sin R

Triangle PQR, right angle at Q. Angle R is at the top right.

Opposite side to angle R = PQ = 7
Hypotenuse = PR = 25

So,
sin R = opposite / hypotenuse = 7 / 25

→ Answer: 7/25

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3) cos X

Triangle XYZ, right angle at Y. Angle X is at the bottom left.

Adjacent side to angle X = XY = 16
Hypotenuse = XZ = 34

So,
cos X = adjacent / hypotenuse = 16 / 34

Simplify: divide numerator and denominator by 2 → 8/17

→ Answer: 8/17

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4) tan S

Triangle STU, right angle at T. Angle S is at the top.

Opposite side to angle S = TU = 24
Adjacent side to angle S = ST = 7

So,
tan S = opposite / adjacent = 24 / 7

Already simplified.

→ Answer: 24/7

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5) sin D

Triangle DEF, right angle at E. Angle D is at the bottom left.

Opposite side to angle D = EF = 12
Hypotenuse = DF = 13

So,
sin D = opposite / hypotenuse = 12 / 13

→ Answer: 12/13

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6) cos A

Triangle ABC, right angle at C. Angle A is at the bottom left.

Adjacent side to angle A = AC = 20
Hypotenuse = AB = 29

So,
cos A = adjacent / hypotenuse = 20 / 29

Already simplified.

→ Answer: 20/29

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Final Answer:
1) 28/45
2) 7/25
3) 8/17
4) 24/7
5) 12/13
6) 20/29