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ere are the lentghs of \( \mathrm{a}, \mathrm{b} \), and c and the angles \( \alpha \) and \( \theta \) 1. Determine a scale factor that will allow you to draw it in a way that uses up most of the paper below. Your scale factor: [3 pts] 2. Make a scale drawing of the property in the space below. Label all sides in ft (not cm ) [5 pts] 245 ff Determine the length of the side marked by the letter X . [3 pts] (Full credit if within plus or m 3\%.)

Ask by Newton Rodriguez. in the United States
Mar 14,2025

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To determine the scale factor, calculate the minimum of the paper's width and height divided by the longest side. Then, use this scale to draw the triangle, labeling all sides in feet. Finally, apply the Law of Cosines or Sines to find the length of side \( X \), ensuring it's within 3% of the calculated value.

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Bonus Knowledge

To tackle this task, we need to first find an appropriate scale factor that maximizes the use of the paper space available while maintaining the proportions of the lengths \( \mathrm{a}, \mathrm{b}, \) and \( c \). If we're working with lengths in feet, consider the maximum width of your drawing area (in feet) compared to the lengths of the lines you want to plot. A simple formula is: \[ \text{Scale Factor} = \frac{\text{Width of Paper}}{\text{Longest Side Length}} \] This ensures the longest side fits perfectly within the space! Next up, for your drawing, ensure you maintain consistent scaling throughout. If you use a scale factor of, say, \( \frac{1}{20} \), then a length of 20 ft should be drawn as 1 in. When it comes to labeling sides, make sure to indicate the scale used. For the side marked \( X \), if you're applying the scale accurately and using geometry (like the sine or cosine laws depending on your shape) to solve for \( X \), ensure to double-check your calculations for a result within ±3%. Take your time, measure twice, and draw once!

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