Final answer:
Writing a fraction of the vertical length over the horizontal length of a triangle creates a ratio representing the triangle's slope. Ratios and proportions are used to relate scale models to actual sizes and can be adapted for different units like feet or inches. Proportions help find unknown scale lengths by relating known measurements via equivalent ratios.
Step-by-step explanation:
When writing a fraction that sets the vertical length of a larger triangle over its horizontal length, you are essentially creating a ratio that represents the slope or steepness of the triangle. In geometry, such a ratio is significant as it defines the relationship between two sides of a right-angled triangle and can be used to determine the triangle's shape.
Scale and Actual Length Ratios
The ratio that represents the actual length of the wingspan to the unknown scale length can be written as scale/actual. For example, if the actual wingspan is 20 feet and the scale model's wingspan is 2 feet, the ratio would be 1/10.
Proportions Using Given Units
To write proportions, you must equate the ratios of equivalent scale and actual measurements. For instance, if the length unit is feet, and the scale length is 0.5 feet representing 5 feet, you would write the proportion as 1/50 = 0.5/5. If the unit is inches, you would adjust your ratios accordingly to maintain consistent units.
Unknown Scale Length
For finding an unknown scale length, you would set up a proportion using a known ratio alongside the unknown one. If the given ratio is 0.5 inches/75 miles and the scale length is 3 inches, the unknown length proportion would be 0.5 inches/75 miles = 3 inches/x miles, where x is the unknown actual length in miles.