Trigonometry Worksheets | Free - CommonCoreSheets - Free Printable

Let’s go through each triangle one by one. We’re looking for three sides relative to angle a:

- Opposite: the side *across from* angle a (not touching it, except at the vertex)
- Adjacent: the side *next to* angle a that is NOT the hypotenuse
- Hypotenuse: the longest side — always across from the right angle

We’ll label them for each problem.

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1)
Angle a is at the bottom right.
Right angle is at bottom left.
So:
→ Opposite = 8 (across from a)
→ Adjacent = 3 (next to a, not hypotenuse)
→ Hypotenuse = φ (longest side, across from right angle)

Wait — actually, in diagram 1, the side labeled “φ” is opposite the right angle? Let me check again.

Actually, looking carefully:
In triangle 1:
- Right angle is at bottom left corner.
- Angle a is at bottom right.
- So side opposite angle a is the vertical side → length 8
- Side adjacent to angle a is the horizontal base → length 3
- Hypotenuse is the slanted side → labeled φ

✔ So:
Opposite = 8
Adjacent = 3
Hypotenuse = φ

But wait — usually we use numbers or letters consistently. Maybe φ is meant to be the hypotenuse label? Yes.

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2)
Angle a is at top left.
Right angle is at bottom right.
Sides:
- Opposite to a: the side across from it → 5
- Adjacent to a: the side next to it (not hypotenuse) → 9
- Hypotenuse: 10.3 (longest side, across from right angle)

✔ Opposite = 5
Adjacent = 9
Hypotenuse = 10.3

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3)
Angle a is at top right.
Right angle is at top left.
Sides:
- Opposite to a: side across from it → 5
- Adjacent to a: side next to it (not hypotenuse) → 6
- Hypotenuse: 7.8 (across from right angle)

✔ Opposite = 5
Adjacent = 6
Hypotenuse = 7.8

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4)
Angle a is at top left.
Right angle is at top right.
Sides:
- Opposite to a: side across from it → 8
- Adjacent to a: side next to it (not hypotenuse) → 7
- Hypotenuse: 10.6 (across from right angle)

✔ Opposite = 8
Adjacent = 7
Hypotenuse = 10.6

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5)
Angle a is at bottom right.
Right angle is at top right.
Sides:
- Opposite to a: side across from it → 6
- Adjacent to a: side next to it (not hypotenuse) → 3
- Hypotenuse: 6.7 (across from right angle)

✔ Opposite = 6
Adjacent = 3
Hypotenuse = 6.7

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6)
Angle a is at bottom left.
Right angle is at top left.
Sides:
- Opposite to a: side across from it → 3
- Adjacent to a: side next to it (not hypotenuse) → 5
- Hypotenuse: 5.8 (across from right angle)

✔ Opposite = 3
Adjacent = 5
Hypotenuse = 5.8

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7)
Angle a is at top left.
Right angle is at bottom left.
Sides:
- Opposite to a: side across from it → 7
- Adjacent to a: side next to it (not hypotenuse) → 8
- Hypotenuse: 10.6 (across from right angle)

✔ Opposite = 7
Adjacent = 8
Hypotenuse = 10.6

---

8)
Angle a is at top.
Right angle is at bottom left.
Sides:
- Opposite to a: side across from it → 3
- Adjacent to a: side next to it (not hypotenuse) → 7
- Hypotenuse: 7.6 (across from right angle)

✔ Opposite = 3
Adjacent = 7
Hypotenuse = 7.6

---

9)
Angle a is at bottom right.
Right angle is at bottom left.
Sides:
- Opposite to a: side across from it → 5
- Adjacent to a: side next to it (not hypotenuse) → 7
- Hypotenuse: 8.6 (across from right angle)

✔ Opposite = 5
Adjacent = 7
Hypotenuse = 8.6

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10)
Angle a is at bottom left.
Right angle is at bottom right.
Sides:
- Opposite to a: side across from it → 8
- Adjacent to a: side next to it (not hypotenuse) → 5
- Hypotenuse: 9.4 (across from right angle)

✔ Opposite = 8
Adjacent = 5
Hypotenuse = 9.4

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11)
Angle a is at top right.
Right angle is at top left.
Sides:
- Opposite to a: side across from it → 5
- Adjacent to a: side next to it (not hypotenuse) → 6
- Hypotenuse: 7.8 (across from right angle)

✔ Opposite = 5
Adjacent = 6
Hypotenuse = 7.8

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12)
Angle a is at left end.
Right angle is at top middle.
Sides:
- Opposite to a: side across from it → 3
- Adjacent to a: side next to it (not hypotenuse) → 8
- Hypotenuse: 8.5 (across from right angle)

✔ Opposite = 3
Adjacent = 8
Hypotenuse = 8.5

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13)
Angle a is at bottom right.
Right angle is at top right.
Sides:
- Opposite to a: side across from it → 8
- Adjacent to a: side next to it (not hypotenuse) → 6
- Hypotenuse: 10.0 (across from right angle)

✔ Opposite = 8
Adjacent = 6
Hypotenuse = 10.0

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14)
Angle a is at bottom.
Right angle is at top.
Sides:
- Opposite to a: side across from it → 3
- Adjacent to a: side next to it (not hypotenuse) → 7
- Hypotenuse: 7.6 (across from right angle)

✔ Opposite = 3
Adjacent = 7
Hypotenuse = 7.6

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15)
Angle a is at top.
Right angle is at bottom right.
Sides:
- Opposite to a: side across from it → 4
- Adjacent to a: side next to it (not hypotenuse) → 8
- Hypotenuse: 8.9 (across from right angle)

✔ Opposite = 4
Adjacent = 8
Hypotenuse = 8.9

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Now let’s list all answers in order:

1) Opp=8, Adj=3, Hyp=φ
2) Opp=5, Adj=9, Hyp=10.3
3) Opp=5, Adj=6, Hyp=7.8
4) Opp=8, Adj=7, Hyp=10.6
5) Opp=6, Adj=3, Hyp=6.7
6) Opp=3, Adj=5, Hyp=5.8
7) Opp=7, Adj=8, Hyp=10.6
8) Opp=3, Adj=7, Hyp=7.6
9) Opp=5, Adj=7, Hyp=8.6
10) Opp=8, Adj=5, Hyp=9.4
11) Opp=5, Adj=6, Hyp=7.8
12) Opp=3, Adj=8, Hyp=8.5
13) Opp=8, Adj=6, Hyp=10.0
14) Opp=3, Adj=7, Hyp=7.6
15) Opp=4, Adj=8, Hyp=8.9

Note: In #1, “φ” is likely meant to be the hypotenuse label — perhaps a typo or placeholder. Since no number is given, we keep it as φ.

Final Answer:
1) Opposite: 8, Adjacent: 3, Hypotenuse: φ
2) Opposite: 5, Adjacent: 9, Hypotenuse: 10.3
3) Opposite: 5, Adjacent: 6, Hypotenuse: 7.8
4) Opposite: 8, Adjacent: 7, Hypotenuse: 10.6
5) Opposite: 6, Adjacent: 3, Hypotenuse: 6.7
6) Opposite: 3, Adjacent: 5, Hypotenuse: 5.8
7) Opposite: 7, Adjacent: 8, Hypotenuse: 10.6
8) Opposite: 3, Adjacent: 7, Hypotenuse: 7.6
9) Opposite: 5, Adjacent: 7, Hypotenuse: 8.6
10) Opposite: 8, Adjacent: 5, Hypotenuse: 9.4
11) Opposite: 5, Adjacent: 6, Hypotenuse: 7.8
12) Opposite: 3, Adjacent: 8, Hypotenuse: 8.5
13) Opposite: 8, Adjacent: 6, Hypotenuse: 10.0
14) Opposite: 3, Adjacent: 7, Hypotenuse: 7.6
15) Opposite: 4, Adjacent: 8, Hypotenuse: 8.9