The distance traveled by the end of the pendulum that swings through an angle of 85 degrees is calculated using trigonometry and comes out to be approximately 23.7 cm when rounded to one decimal place.
To calculate the distance that the end of a pendulum travels when it swings through an angle, we need to use the concept of arc length in trigonometry.
Given that the pendulum length is 16 cm and the angle through which it swings is 85 degrees, we can use the formula for arc length S = rθ, where S is the arc length, r is the radius or length of the pendulum, and θ is the angle in radians.
First, convert the angle from degrees to radians by multiplying it by π/180. Thus, 85 degrees × π/180 = 1.4835 radians approximately. Next, apply the formula: S = 16 cm × 1.4835 = 23.736 cm. This is the distance traveled by the pendulum, which we round to 23.7 cm (1 decimal place).