Final answer:
To find the radius of the grain storage silo, we use the measurements given along with the Pythagorean theorem, taking into account the length of the straightedge and the measured 'H' distance. The radius is calculated using the formula R = (H^2 + (C/2)^2) / (2*H), which gives us approximately 76.784 inches for the radius of the silo.
Step-by-step explanation:
The student is asking how to find the radius of a silo given certain measurements when using a 10' long strut as a straightedge. Since the strut is 10 feet long, which is equal to 120 inches, we can visualize forming a chord across the silo with the strut.
The distance from the ends of the strut to the wall of the silo is measured at 14 3/4" on each side. This distance, known as the "H" distance, forms two right-angle triangles with the centerline of the silo, which is also the radius we are looking to find.
To calculate the radius (R), we can use the Pythagorean theorem. The total length of the strut minus twice the "H" distance gives us the length of the chord (C). The radius can be found through the relationship R = (H^2 + (C/2)^2) / (2*H), where H is the sagitta or the perpendicular distance from the chord to the center of the circle (the radius line), and C is the chord length. Plugging in the values:
- Length of straightedge (total strut length), L = 120 inches
- Distance H from the end of the straightedge to the wall, H = 14.75 inches
- Chord length, C = L - 2*H = 120 inches - 2*(14.75 inches) = 90.5 inches
Substituting the values into the equation, we get:
R = ((14.75)^2 + (90.5/2)^2) / (2*14.75)
Carrying out the calculation:
R = ((217.5625) + (45.25)^2) / (29.5)
R = (217.5625 + 2047.5625) / 29.5
R = 2265.125 / 29.5
R = 76.784 (approximately)
Therefore, the radius of the silo is approximately 76.784 inches.