Final answer:
To find the unlabeled sides of a right triangle, use the Pythagorean theorem, which is s² = D² + L². For understanding scale ratios, actual lengths can be found by multiplying the scale model lengths by their respective scale factors. Setting up proportions can help to compare corresponding lengths of scaled objects.
Step-by-step explanation:
To calculate the lengths of the 2 unlabeled sides, represented as D (depth) and L (length), in a right triangle with hypotenuse s, we can apply the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (s) is equal to the sum of the squares of the lengths of the other two sides (D and L). The formula is s2 = D2 + L2. Once we have the measures of D, L, and s, we can manipulate this equation to find the unknown sides.
For understanding scales and proportions, if a problem states that a scale/actual ratio is 1/20 for a wingspan, it means that the actual length of the wingspan is 20 times larger than the scale model. Similarly, if a scale/actual ratio is 1/5.5 for a side, the actual length of the side is 5.5 times larger than the scale model. To find the actual lengths, we multiply the scale lengths by the respective scale factors.
Proportions and Scale Factors
To determine corresponding sides on different scaled objects, you can set up proportions that compare their lengths. If a larger square has sides that are twice the length of a smaller square's sides, the scale factor is 2. Therefore, if the smaller square has a side length of 4 inches, the larger square's side will be 4 inches x 2 = 8 inches. A proportion between the small and large squares' sides will be 4/8 or 1/2.