Right Triangle Trigonometry Notes and Worksheets - Lindsay Bowden - Free Printable

Here is the complete solution to the “Intro to Trigonometry Practice” worksheet. For each right triangle, we use the basic trigonometric ratios:

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

All fractions are reduced to lowest terms.

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1. Triangle ABC (right angle at B)

Sides: AB = 9, BC = 12, AC = 15 (hypotenuse)

For 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

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2. Triangle DEF (right angle at D)

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

For 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

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3. Triangle QRS (right angle at R)

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

For 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

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4. Triangle MNO (right angle at N)

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

For 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

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5. Triangle TUV (right angle at U)

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

For 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

For 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

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6. Triangle GHI (right angle at H)

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

For 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

For 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

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7. Triangle FGH (right angle at G)

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

For 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

For 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

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8. Triangle RST (right angle at S)

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

For 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

For 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

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✔ All answers are reduced to lowest terms as required.

Let me know if you’d like a diagram or explanation for any specific problem!