Final answer:
To find the length of the side labeled x, we can use the given information and the concept of similar triangles. By setting up a proportion using the ratios of corresponding side lengths of similar triangles, we can solve for x. The length of x is approximately 0.04 miles.
Step-by-step explanation:
To find the length of the side labeled x, we can use the given information and the concept of similar triangles. We have a triangle with angles measuring 44°, 32°, and 43°. Since the angles in a triangle add up to 180°, we can find the remaining angle by subtracting the sum of the given angles from 180°. In this case, the remaining angle is 180° - (44° + 32° + 43°) = 61°.
Now, we can set up a proportion using the ratios of corresponding side lengths of similar triangles. The known length of 8 inches corresponds to the known length of 20 miles. The unknown length of x corresponds to the unknown length of the side in miles. So, we have the proportion:
8 inches / 20 miles = x inches / y miles
Cross-multiplying and solving for x, we have:
8 inches * y miles = 20 miles * x inches
y miles = (20 miles * x inches) / 8 inches
Converting inches to miles, we divide by 63,360 inches in a mile:
y miles = (20 miles * x inches) / 8 inches / 63,360 inches/mile
Simplifying, we get:
y miles = 0.0003968253968253968 * x inches
To find the length of x in miles, we substitute y = 1 (since x corresponds to the side in miles) into the equation:
1 = 0.0003968253968253968 * x inches
Solving for x, we get:
x = 1 / 0.0003968253968253968
x ≈ 2520 inches
Rounding to the nearest tenth, we get x ≈ 2520 / 63360 ≈ 0.04 miles.