Trigonometry worksheet showing triangle PQR with angle measures and side lengths, requiring completion of sine, cosine, and tangent values.

Let’s solve this step by step.

We are given triangle PQR, which is a right triangle (right angle at R).
Angles:
- ∠P = 53.2°
- ∠Q = 36.8°
Sides:
- Side opposite to ∠P (which is QR) = 4
- Side adjacent to ∠P (which is PR) = 3
- Hypotenuse (PQ) = 5

We need to fill in the trig ratios for each angle using:

- Sine = opposite / hypotenuse
- Cosine = adjacent / hypotenuse
- Tangent = opposite / adjacent

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For angle 53.2° (∠P):

- Opposite side = QR = 4
- Adjacent side = PR = 3
- Hypotenuse = PQ = 5

So:
- Sine = 4/5 = 0.8
- Cosine = 3/5 = 0.6
- Tangent = 4/3 ≈ 1.333...

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For angle 36.8° (∠Q):

Now, from ∠Q’s perspective:
- Opposite side = PR = 3 (because it’s across from Q)
- Adjacent side = QR = 4 (next to Q, not the hypotenuse)
- Hypotenuse = still PQ = 5

So:
- Sine = 3/5 = 0.6
- Cosine = 4/5 = 0.8
- Tangent = 3/4 = 0.75

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Double-check:
In a right triangle, sin(θ) = cos(90° - θ), and tan(θ) = 1/tan(90° - θ).
Here, 53.2° + 36.8° = 90°, so they’re complementary.
→ sin(53.2°) should equal cos(36.8°) → 0.8 = 0.8 ✔️
→ cos(53.2°) should equal sin(36.8°) → 0.6 = 0.6 ✔️
→ tan(53.2°) = 4/3 ≈ 1.333, tan(36.8°) = 3/4 = 0.75 → and 1.333 × 0.75 = 1 ✔️

All checks out.

Final Answer:
| Measure of Angle | Sine (opp/hyp) | Cosine (adj/hyp) | Tangent (opp/adj) |
|------------------|----------------|------------------|-------------------|
| 53.2 | 0.8 | 0.6 | 1.333 |
| 36.8 | 0.6 | 0.8 | 0.75 |