The pendulum of a grandfather clock is 90cm long. When the pendulum swings from side to side, it travels a horizontal distance of 9.2cm. Determine the angle through which the pendulum swings. Round your answer to the nearest degree

tan(Θ/2) = (9.2 / 2) / 90

Θ = ?

To determine the angle through which the pendulum swings, we can use the formula for the arc length of a pendulum:

Arc Length (s) = R * θ,

where
R is the length of the pendulum (90 cm in this case),
θ is the angle through which the pendulum swings, and
s is the horizontal distance traveled by the pendulum (9.2 cm in this case).

Rearranging the formula to solve for θ, we have:

θ = s / R.

Plugging in the given values, we get:

θ = 9.2 cm / 90 cm.

Calculating this, we find:

θ ≈ 0.1022.

Now, to convert this into degrees, we simply multiply by 180 and divide by π:

θ (in degrees) ≈ (0.1022 * 180) / π.

Calculating this, we find:

θ (in degrees) ≈ 5.8526.

Rounding this to the nearest degree, we have:

θ ≈ 6 degrees.

Therefore, the angle through which the pendulum swings is approximately 6 degrees.

To determine the angle through which the pendulum swings, we can use the formula for the arc length of a pendulum:

Arc Length = Radius * Angle

In this case, the radius of the pendulum is the length of the pendulum itself, which is given as 90 cm. The arc length is the horizontal distance traveled by the pendulum, which is given as 9.2 cm.

Plugging these values into the formula, we can calculate the angle:

9.2 cm = 90 cm * Angle

Now, let's solve the equation for Angle:

Angle = 9.2 cm / 90 cm

Angle = 0.1022

To convert this angle to degrees, we'll multiply it by 180 and round to the nearest degree:

Angle (in degrees) = 0.1022 * 180

Angle (in degrees) = 18.396

Rounding this value to the nearest degree, we get:

Angle (rounded to the nearest degree) ≈ 18 degrees

Therefore, the angle through which the pendulum swings is approximately 18 degrees.