Trigonometry practice worksheet with eight right triangles for calculating sine, cosine, and tangent ratios.

Let’s solve each problem step by step. We’re working with right triangles, and we need to find sine, cosine, and tangent for the given angles.

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

Also: The hypotenuse is always the longest side — it’s across from the right angle.

We’ll go one triangle at a time.

---

Problem 1: Triangle ABC (right angle at B)
Sides: AB = 9, BC = 12, AC = 15 → hypotenuse is AC = 15

Angle A:
- Opposite to A: BC = 12
- Adjacent to A: AB = 9
- Hypotenuse: AC = 15

→ sin(A) = 12/15 = 4/5
→ cos(A) = 9/15 = 3/5
→ tan(A) = 12/9 = 4/3

✔ Reduced fractions.

---

Problem 2: Triangle DEF (right angle at D)
Sides: DF = 12, DE = 16, EF = 20 → hypotenuse is EF = 20

Angle F:
- Opposite to F: DE = 16
- Adjacent to F: DF = 12
- Hypotenuse: EF = 20

→ sin(F) = 16/20 = 4/5
→ cos(F) = 12/20 = 3/5
→ tan(F) = 16/12 = 4/3

✔ Reduced.

---

Problem 3: Triangle QRS (right angle at R)
Sides: QR = 5, RS = 12, QS = 13 → hypotenuse is QS = 13

Angle Q:
- Opposite to Q: RS = 12
- Adjacent to Q: QR = 5
- Hypotenuse: QS = 13

→ sin(Q) = 12/13
→ cos(Q) = 5/13
→ tan(Q) = 12/5

✔ Already reduced.

---

Problem 4: Triangle MNO (right angle at N)
Sides: MN = 24, NO = 10, MO = 26 → hypotenuse is MO = 26

Angle M:
- Opposite to M: NO = 10
- Adjacent to M: MN = 24
- Hypotenuse: MO = 26

→ sin(M) = 10/26 = 5/13
→ cos(M) = 24/26 = 12/13
→ tan(M) = 10/24 = 5/12

✔ Reduced.

---

Problem 5: Triangle TUV (right angle at U)
Sides: TU = 3, UV = 4, TV = 5 → hypotenuse is TV = 5

First, angle V:
- Opposite to V: TU = 3
- Adjacent to V: UV = 4
- Hypotenuse: TV = 5

→ sin(V) = 3/5
→ cos(V) = 4/5
→ tan(V) = 3/4

Now angle T:
- Opposite to T: UV = 4
- Adjacent to T: TU = 3
- Hypotenuse: TV = 5

→ sin(T) = 4/5
→ cos(T) = 3/5
→ tan(T) = 4/3

✔ All reduced.

---

Problem 6: Triangle GHI (right angle at H)
Sides: GH = 9, HI = 40, GI = 41 → hypotenuse is GI = 41

Angle G:
- Opposite to G: HI = 40
- Adjacent to G: GH = 9
- Hypotenuse: GI = 41

→ sin(G) = 40/41
→ cos(G) = 9/41
→ tan(G) = 40/9

Angle I:
- Opposite to I: GH = 9
- Adjacent to I: HI = 40
- Hypotenuse: GI = 41

→ sin(I) = 9/41
→ cos(I) = 40/41
→ tan(I) = 9/40

✔ All reduced.

---

Problem 7: Triangle FGH (right angle at G)
Sides: FG = 8, GH = 15, FH = 17 → hypotenuse is FH = 17

Angle F:
- Opposite to F: GH = 15
- Adjacent to F: FG = 8
- Hypotenuse: FH = 17

→ sin(F) = 15/17
→ cos(F) = 8/17
→ tan(F) = 15/8

Angle H:
- Opposite to H: FG = 8
- Adjacent to H: GH = 15
- Hypotenuse: FH = 17

→ sin(H) = 8/17
→ cos(H) = 15/17
→ tan(H) = 8/15

✔ All reduced.

---

Problem 8: Triangle RST (right angle at S)
Sides: RS = 12, ST = 35, RT = 37 → hypotenuse is RT = 37

Angle R:
- Opposite to R: ST = 35
- Adjacent to R: RS = 12
- Hypotenuse: RT = 37

→ sin(R) = 35/37
→ cos(R) = 12/37
→ tan(R) = 35/12

Angle T:
- Opposite to T: RS = 12
- Adjacent to T: ST = 35
- Hypotenuse: RT = 37

→ sin(T) = 12/37
→ cos(T) = 35/37
→ tan(T) = 12/35

✔ All reduced.

---

Final Answer:

1.
sin(A) = 4/5
cos(A) = 3/5
tan(A) = 4/3

2.
sin(F) = 4/5
cos(F) = 3/5
tan(F) = 4/3

3.
sin(Q) = 12/13
cos(Q) = 5/13
tan(Q) = 12/5

4.
sin(M) = 5/13
cos(M) = 12/13
tan(M) = 5/12

5.
sin(V) = 3/5, sin(T) = 4/5
cos(V) = 4/5, cos(T) = 3/5
tan(V) = 3/4, tan(T) = 4/3

6.
sin(G) = 40/41, sin(I) = 9/41
cos(G) = 9/41, cos(I) = 40/41
tan(G) = 40/9, tan(I) = 9/40

7.
sin(F) = 15/17, sin(H) = 8/17
cos(F) = 8/17, cos(H) = 15/17
tan(F) = 15/8, tan(H) = 8/15

8.
sin(R) = 35/37, sin(T) = 12/37
cos(R) = 12/37, cos(T) = 35/37
tan(R) = 35/12, tan(T) = 12/35