Compare customary units by multiplying

Learning Objectives Apply trigonometric ratios (SOH CAH TOA) to find unknown side lengths in right triangles. Identify the correct customary unit conversion factor (e.g., inches, feet, yards). Convert a measurement from a larger customary unit to a smaller customary unit by multiplying. Solve multi-step right triangle problems that require a final unit conversion. Use the Pythagorean theorem to find a side length and then convert its units by multiplying. Verify the reasonableness of an answer after converting units within a geometric context. Set up and solve word problems involving right triangles where initial and final units differ. An architect designs a wheelchair ramp that is 2 yards long. How can you use trigonometry and multiplication to find its height in inches?...

TermDefinitionExample Customary Units of LengthThe system of measurement for length used primarily in the United States. Key units include inches (in), feet (ft), yards (yd), and miles (mi).A standard door is about 7 feet tall. A football field is 100 yards long. Conversion FactorA number used to change one set of units to another by multiplying or dividing. When converting from a larger unit to a smaller unit, you multiply.The conversion factor to change feet to inches is 12, because there are 12 inches in 1 foot. Dimensional AnalysisA problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is used to convert units by multiplying with conversion factors expressed as fractions.To convert 5 feet to inches: 5 \text{ ft}...

Feet to Inches Conversion L_{in} = L_{ft} \times 12 To convert a length from feet (L_{ft}) to inches (L_{in}), multiply the number of feet by 12. Yards to Feet Conversion L_{ft} = L_{yd} \times 3 To convert a length from yards (L_{yd}) to feet (L_{ft}), multiply the number of yards by 3. Yards to Inches Conversion L_{in} = L_{yd} \times 36 To convert a length from yards (L_{yd}) to inches (L_{in}), multiply the number of yards by 36. This is a two-step conversion (yards to feet, then feet to inches) combined into one. Pythagorean Theorem a^2 + b^2 = c^2 Used in a right triangle to find the length of a third side when two sides are known. 'a' and 'b' are the legs, and 'c' is the hypotenuse. The units must be consistent for all sid...