Final answer:
In a right triangle, the side lengths can be determined using the Pythagorean theorem. For scale drawings, the actual lengths can be multiplied by the scale factor to find the scaled lengths. Trigonometry allows for measurement of angles and sides to solve triangles.
Step-by-step explanation:
To identify the side lengths of a triangle, specifically a right triangle, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we denote these two sides as D and L, and the hypotenuse as s, the equation would be D2 + L2 = s2.
When dealing with a scale drawing, such as the one Leah is making of a flower bed with a longest side of 5.5 meters and a scale factor of 1/20, we simply multiply the actual length by the scale factor to get the scaled length. In this case, the length of the longest side in her drawing will be 5.5 meters × 1/20 = 0.275 meters or 27.5 centimeters.
Trigonometry is also a useful tool for determining the magnitude and direction of vector components by measuring angles with respect to a reference frame, as mentioned in the context of measuring angles and sides in triangles. Using the trigonometric definitions of sine, cosine, and tangent in relation to the lengths of a right triangle's sides can help resolve these components efficiently.