A = π (x tan 30°)^2 / 4
Process:
- Put the triangle on a cartesian plane with the lower left point at the origin (0, 0) and the lower edge along the x axis.
- Draw line L from the lower-left corner of the triangle to the midpoint of the opposite edge.
- This passes through the common center point of the large circle and triangle
- Determine the slope of L:
- The angle of L from the horizon must be 30 degrees; it is half of 60, which is the inner angle of each corner of an equilateral triangle, by definition.
- The slope of a line at an angle is given by the trigonometric tangeant function, which is defined as the ratio of the opposite side (y) to the adjacent side (x).
- Therefore, the slope of L is tan 30°
- Determine the y coordinate of L when x is 1/2. This will give the radius of the circle.
- The slope formula for a line is y = mx + b where y is the unknown y coordinate, m is the slope, x is the x coordinate, and b is the value of y where the line intersects with the y axis.
- Therefore, radius = (x tan 30°) / 2
- So A = π (x tan 30°)^2 / 4
B = ?
Process:
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