Triangle Calculations
1. **Problem 1: Calculate the value of p in the right triangle with angle 60° and adjacent side 10 cm, given Tan 60° = 1.7.**
2. Recall the tangent definition: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$.
3. Substitute the known values: $$1.7 = \frac{p}{10}$$.
4. Solve for $$p$$: $$p = 1.7 \times 10 = 17$$ cm.
5. **Problem 2: Calculate the area of the triangle with sides 10 cm and 20 cm and included angle 45°, using Area = \frac{1}{2}ab\sin C, and Sin 45° = 0.707.**
6. Substitute the values into the formula:
$$\text{Area} = \frac{1}{2} \times 10 \times 20 \times 0.707$$.
7. Calculate step-by-step:
$$\frac{1}{2} \times 10 = 5$$,
$$5 \times 20 = 100$$,
$$100 \times 0.707 = 70.7$$ cm².
**Final answers:**
- $$p = 17$$ cm
- Area = $$70.7$$ cm²