Introduction to Trigonometry - Go Teach Maths: Handcrafted - Free Printable

Here is the complete solution for all 8 problems on the “Intro to Trigonometry Practice” worksheet. For each right triangle, we use the definitions:

- sin(θ) = Opposite / Hypotenuse
- cos(θ) = Adjacent / Hypotenuse
- tan(θ) = Opposite / Adjacent

We reduce all fractions to lowest terms.

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1. Triangle ABC (right angle at B)

Sides: AB = 9 (opposite to C, adjacent to A), BC = 12 (adjacent to C, opposite to A), AC = 15 (hypotenuse)

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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2. Triangle DEF (right angle at D)

Sides: DE = 16, DF = 12, EF = 20 (hypotenuse)

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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3. Triangle QRS (right angle at R)

Sides: QR = 5, RS = 12, QS = 13 (hypotenuse)

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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4. Triangle MNO (right angle at N)

Sides: MN = 24, NO = 10, MO = 26 (hypotenuse)

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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5. Triangle TUV (right angle at U)

Sides: TU = 3, UV = 4, TV = 5 (hypotenuse)

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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6. Triangle GHI (right angle at H)

Sides: GH = 9, HI = 40, GI = 41 (hypotenuse)

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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7. Triangle FGH (right angle at G)

Sides: FG = 8, GH = 15, FH = 17 (hypotenuse)

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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8. Triangle RST (right angle at S)

Sides: RS = 12, ST = 35, RT = 37 (hypotenuse)

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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✔ All answers are reduced to lowest terms as instructed.

Let me know if you’d like a diagram or mnemonic to remember SOH-CAH-TOA!