Intro to Trigonometry Practice worksheet featuring eight right triangles with side lengths and angles for calculating trigonometric ratios.

I'll solve this trigonometry worksheet step by step, finding the sine, cosine, and tangent ratios for each angle in the right triangles.

Key formulas to remember:
- sin(θ) = opposite/hypotenuse
- cos(θ) = adjacent/hypotenuse
- tan(θ) = opposite/adjacent

Let me work through each problem:

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Problem 1: Triangle ABC (right angle at B)
- Sides: AB = 9, BC = 12, AC = 15
- For angle A: opposite = BC = 12, adjacent = AB = 9, hypotenuse = AC = 15

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

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Problem 2: Triangle DEF (right angle at D)
- Sides: DF = 12, DE = 16, EF = 20
- For angle F: opposite = DE = 16, adjacent = DF = 12, hypotenuse = EF = 20

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

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Problem 3: Triangle QRS (right angle at R)
- Sides: QR = 5, RS = 12, QS = 13
- For angle Q: opposite = RS = 12, adjacent = QR = 5, hypotenuse = QS = 13

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

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Problem 4: Triangle MNO (right angle at N)
- Sides: MN = 24, NO = 10, MO = 26
- For angle M: opposite = NO = 10, adjacent = MN = 24, hypotenuse = MO = 26

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

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

For angle V: opposite = TU = 3, adjacent = UV = 4, hypotenuse = TV = 5
sin(V) = 3/5
cos(V) = 4/5
tan(V) = 3/4

For angle T: opposite = UV = 4, adjacent = TU = 3, hypotenuse = TV = 5
sin(T) = 4/5
cos(T) = 3/5
tan(T) = 4/3

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

For angle G: opposite = HI = 40, adjacent = GH = 9, hypotenuse = GI = 41
sin(G) = 40/41
cos(G) = 9/41
tan(G) = 40/9

For angle I: opposite = GH = 9, adjacent = HI = 40, hypotenuse = GI = 41
sin(I) = 9/41
cos(I) = 40/41
tan(I) = 9/40

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

For angle F: opposite = GH = 15, adjacent = FG = 8, hypotenuse = FH = 17
sin(F) = 15/17
cos(F) = 8/17
tan(F) = 15/8

For angle H: opposite = FG = 8, adjacent = GH = 15, hypotenuse = FH = 17
sin(H) = 8/17
cos(H) = 15/17
tan(H) = 8/15

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

For angle R: opposite = ST = 35, adjacent = RS = 12, hypotenuse = RT = 37
sin(R) = 35/37
cos(R) = 12/37
tan(R) = 35/12

For angle T: opposite = RS = 12, adjacent = ST = 35, hypotenuse = RT = 37
sin(T) = 12/37
cos(T) = 35/37
tan(T) = 12/35

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

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

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

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