The side of a regular hexagon is 10 mm. What is the across flat t

SOLUTION

Concept:

If you draw the three diagonals in a regular hexagon the hexagon is divided into six equilateral triangles.

The length of one side of hexagon = 10 mm

LAMI’S Theorem states, “If three coplanar forces acting at a point be in equilibrium, then each force is proportional to the sine of the angle between the other two.”

Consider three forces F1, F2, F3 acting on a particle or rigid body making angles α, β, and γ with each other.

Mathematically, \(\frac{{{F_1}}}{{\sin \alpha }} = \frac{{{F_2}}}{{\sin \beta }} = \frac{{{F_3}}}{{\sin \gamma }}\)

Calculation:

Given:

\(\frac{{{5}}}{{\sin 30 }} = \frac{{{x/2}}}{{\sin 60 }} \)

Therefore, x = 10 √3 = 17.32 mm