To solve this problem, we need to use the sine function in trigonometry. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, the opposite side is the distance from the pod P to the x-axis, and the hypotenuse is the radius of the Ferris wheel.

1. Set up the equation: sin(𝜃) = 30/70 = 0.4286

2. Use the inverse sine function to find the angle: 𝜃 = sin^-1(0.4286) = 25.4°

However, because the Ferris wheel rotates 360°, there are two positions where the pod P is 30m from the x-axis. One is measured anti-clockwise from the x-axis (25.4°), and the other is measured clockwise. To find the clockwise angle, subtract 25.4° from 180°:

3. 180° - 25.4° = 154.6°

So, the two angles for which the pod P is 30m from the x-axis are 25.4° and 154.6°.

Question

To solve this problem, we need to use the sine function in trigonometry. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, the opposite side is the distance from the pod P to the x-axis, and the hypotenuse is the radius of the Ferris wheel.

1. Set up the equation: sin(𝜃) = 30/70 = 0.4286

2. Use the inverse sine function to find the angle: 𝜃 = sin^-1(0.4286) = 25.4°

However, because the Ferris wheel rotates 360°, there are two positions where the pod P is 30m from the x-axis. One is measured anti-clockwise from the x-axis (25.4°), and the other is measured clockwise. To find the clockwise angle, subtract 25.4° from 180°:

3. 180° - 25.4° = 154.6°

So, the two angles for which the pod P is 30m from the x-axis are 25.4° and 154.6°.

Knowee AI · Accepted Answer

To solve this problem, we need to use the sine function in trigonometry. The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypotenuse. In this case, the opposite side is the distance from the pod P to the x-axis, and the hypotenuse is the radius of the Ferris wheel.

1. Set up the equation: sin(𝜃) = 30/70 = 0.4286

2. Use the inverse sine function to find the angle: 𝜃 = sin^-1(0.4286) = 25.4°

However, because the Ferris wheel rotates 360°, there are two positions where the pod P is 30m from the x-axis. One is measured anti-clockwise from the x-axis (25.4°), and the other is measured clockwise. To find the clockwise angle, subtract 25.4° from 180°:

3. 180° - 25.4° = 154.6°

So, the two angles for which the pod P is 30m from the x-axis are 25.4° and 154.6°.

Given that the radius of the Ferris wheel is 70m and that 𝜃 represents the angle measured anti-clockwise from the x-axis, find all the angles for which the pod P is 30m from the x-axis. Round to the nearest tenth and list from least to greatest. °°°

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