1) The height of the kite is approximately 106.07 feet.
- This is a right triangle problem where the string is the hypotenuse (150 ft) and the angle with the ground is 45°.
- The height (x) is the side opposite the 45° angle.
- Use the sine function: sin(45°) = opposite/hypotenuse = x/150.
- Solve for x: x = 150 * sin(45°) = 150 * (√2/2) ≈ 150 * 0.7071 ≈ 106.07 feet.
2) The angle of elevation of the sun is approximately 30 degrees.
- This is a right triangle problem where the tree height (10 m) is the opposite side and the shadow length (17.3 m) is the adjacent side.
- Use the tangent function: tan(x°) = opposite/adjacent = 10/17.3.
- Solve for x: x = arctan(10/17.3) ≈ arctan(0.578) ≈ 30°.
Parent Tip: Review the logic above to help your child master the concept of worksheet angles of depression and elevation.
