Subjects geometry

Triangle Calculations

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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