Answer to Question #5220 in Trigonometry for Samuel

Question

The pendulum of an old clock is 90cm long.
It swings from side to side through an angle of 10°.
How wide must the clock case be made so that the pendulum can swing freely?

Answer 1

Let's find the basis of a triangle created by the extreme positions of a pendulum. We can do that by dividing it into two right triangles. So, the case width must be
W = 2*L*sin(α/2) = 2*90*sin(10/2) = 2*90*sin(5°) = 15.69 cm