A decorative pottery bowl with a diameter of 30 cm is used as a garden ornament . A rain shower fills it with water to a maximum depth of 7 cm. The bowl is slowly tipped to remove the water. What angle will the rim of the bowl make with the horizontal when the water begins to spill out?
To find the angle that the rim of the bowl makes with the horizontal when the water begins to spill out, we can use trigonometry.
First, let's draw a diagram to visualize the problem. The bowl can be represented as a circle, and we have a right triangle formed by the radius of the bowl, the height of the water, and the distance from the center of the bowl to the water's edge.
The radius of the bowl is half the diameter, which is 30 cm, so the radius is 15 cm. The height of the water is 7 cm.
Now, let's label the right triangle. We have the radius as the hypotenuse, the height of the water as the opposite side, and the distance from the center to the water's edge as the adjacent side.
Using the trigonometric function tangent (tan), we can write:
tan(angle) = opposite/adjacent
In this case, the opposite side is the height of the water (7 cm), and the adjacent side is half the diameter (15 cm).
Plugging in the values, we get:
tan(angle) = 7/15
To find the angle, we can take the inverse tangent (arctan) of both sides:
angle = arctan(7/15)
Using the inverse tangent function on a calculator or online tool, we find that the angle is approximately 25.25 degrees.
Therefore, the rim of the bowl will make an angle of approximately 25.25 degrees with the horizontal when the water begins to spill out.