Question

A rectangle is 60 cm long and 20 cm wide. Find, to the nearest tenth of a degree, the acute angle formed at the intersection of the diagonals.

Answer 1

36.9°

Explanation:

As shown in the diagram attached,

θ is the acute angle formed at the intersection of the diagonals of the rectangle.

From the diagram,

tan(θ/2) = 10/30

tan(θ/2) = 1/3

θ/2 = tan⁻¹(1/3)

θ/2 = 18.43

Therefore,

θ = 18.43×2

θ = 36.87

θ = 36.9°

Hence the acute angle formed is 36.9°