Final answer:
To find the height of the house, similar triangles are used. Melissa's height is 5 ft with a 4 ft shadow, and the house's shadow is 16 ft. The house is 20 feet tall.
Step-by-step explanation:
At 2:30 pm, Melissa measured her shadow and her house's shadow to determine the height of the house. To solve this problem, we use similar triangles where the ratio of the heights is equal to the ratio of the lengths of the shadows because the sun's rays provide equal angles of elevation for Melissa and her house. Melissa is 5 ft tall and her shadow is 4 ft long. The house's shadow is 16 ft long. To find the height of the house (H), we set up the proportion 5 ft / 4 ft = H / 16 ft.
After cross-multiplying we get: 4 ft * H = 5 ft * 16 ft, which simplifies to H = (5 ft * 16 ft) / 4 ft = 20 ft. Therefore, the height of the house is 20 feet.
Scale and Measurement Review
When working with scale models and maps, it's important to apply the given scale factor to convert real measurements to model sizes and vice versa.
- Haley's scale model: A school building that's 30 feet tall would be 5 inches on her model since 1 inch equals 6 feet. For a width of 120 feet, it would be 20 inches in the scale model, and for a length of 180 feet, it would be 30 inches in the model.
- Eddie's map: If the real distance is 56 meters on a map with a scale of 1 cm equals 8 meters, the mapped distance is 7 cm.
- Juliana's measurement: To measure a 200-centimeter long board with a meter stick, she can use it twice because one meter stick is 100 centimeters.
- Forces on a ladder: When a person climbs on a ladder leaned against a wall, the forces at the top and bottom can be calculated considering the moments around the pivot point, accounting for the weight of the person and the ladder's own weight.