Trigonometric Ratios practice worksheet with right triangles and side lengths.

Let's solve each trigonometric ratio problem one by one, using the definitions of sine, cosine, and tangent in right triangles:

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Recall:

In a right triangle, for angle θ:

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

We’ll identify the correct sides relative to the given angle in each triangle.

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1) tan B = ______

Triangle: Right triangle BHR, right angle at H.

Angle B is at vertex B.

- Opposite to ∠B: side RH = 12
- Adjacent to ∠B: side BH = 9

→ tan B = opposite / adjacent = 12 / 9 = 4/3

✔ Answer: 4/3

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2) cos B = ______

Triangle: Right triangle BST, right angle at S.

Angle B is at vertex B.

- Adjacent to ∠B: side BS = 20
- Hypotenuse: BT = 25

→ cos B = adjacent / hypotenuse = 20 / 25 = 4/5

✔ Answer: 4/5

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3) tan M = ______

Triangle: Right triangle MPT, right angle at P.

Angle M is at vertex M.

- Opposite to ∠M: side PT = 8
- Adjacent to ∠M: side MP = 15

→ tan M = opposite / adjacent = 8 / 15

✔ Answer: 8/15

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4) sin G = ______

Triangle: Right triangle GVM, right angle at V.

Angle G is at vertex G.

- Opposite to ∠G: side VM = 32
- Hypotenuse: GM = 40

→ sin G = opposite / hypotenuse = 32 / 40 = 4/5

✔ Answer: 4/5

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5) tan G = ______

Triangle: Right triangle GYC, right angle at Y.

Angle G is at vertex G.

- Opposite to ∠G: side YC = 15
- Adjacent to ∠G: side GY = 20

→ tan G = opposite / adjacent = 15 / 20 = 3/4

✔ Answer: 3/4

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6) cos C = ______

Triangle: Right triangle CZL, right angle at Z.

Angle C is at vertex C.

- Adjacent to ∠C: side CZ = 28
- Hypotenuse: CL = 35

→ cos C = adjacent / hypotenuse = 28 / 35 = 4/5

✔ Answer: 4/5

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7) tan X = ______

Triangle: Right triangle LRX, right angle at R.

Angle X is at vertex X.

- Opposite to ∠X: side LR = 8
- Adjacent to ∠X: side RX = 15

→ tan X = opposite / adjacent = 8 / 15

✔ Answer: 8/15

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8) sin O = ______

Triangle: Right triangle OBX, right angle at B.

Angle O is at vertex O.

- Opposite to ∠O: side BX = 20
- Hypotenuse: OX = 52

→ sin O = opposite / hypotenuse = 20 / 52 = 5/13

✔ Answer: 5/13

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## ✔ Final Answers:

1) tan B = 4/3
2) cos B = 4/5
3) tan M = 8/15
4) sin G = 4/5
5) tan G = 3/4
6) cos C = 4/5
7) tan X = 8/15
8) sin O = 5/13

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