1. For each of the following, find the third side and the angle labeled:
- First triangle: Third side = √(12² + 11²) = √265 ≈ 16.28; Angle θ = arctan(11/12) ≈ 42.51°
- Second triangle: Third side = √(11² + 8²) = √185 ≈ 13.60; Angle θ = arctan(8/11) ≈ 36.03°
2. Find the other two sides of each triangle:
- First triangle: Opposite side = 10 * sin(30°) = 5; Adjacent side = 10 * cos(30°) = 5√3 ≈ 8.66
- Second triangle: Opposite side = 7 * sin(50°) ≈ 5.36; Adjacent side = 7 * cos(50°) ≈ 4.50
3. Resolve each of the following vectors into horizontal and vertical components. Determine the magnitude of each component vector:
- First vector (20 m at 45°): Horizontal = 20 * cos(45°) = 10√2 ≈ 14.14 m; Vertical = 20 * sin(45°) = 10√2 ≈ 14.14 m
- Second vector (16 m at 30° below horizontal): Horizontal = 16 * cos(30°) = 8√3 ≈ 13.86 m; Vertical = -16 * sin(30°) = -8 m
Parent Tip: Review the logic above to help your child master the concept of vector worksheet.
