# Answer to Question #5220 in Trigonometry for Samuel

Question #5220

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?

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?

Expert's answer

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

W = 2*L*sin(α/2) = 2*90*sin(10/2) = 2*90*sin(5°) = 15.69 cm

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