Question

A rectangle is 4.2 centimetres wide and each diagonal is 8.6 centimetres long. What is the measure of the angle between a diagonal and the shorter side of the rectangle, to the nearest tenth of a degree?

Answer 1

`60.8^\circ`

Explanation:

First, let's check side lengths.

Using the Pythagorean theorem we can find the length of the other side of the rectangle.

a^2 + b^2 = c^2

4.2^2 + b^2 = 8.6^2

b^2 = 56.32

b = 7.5

The other side of the rectangle measures 7.5 cm, so now we know that 4.2 cm is indeed the shorter side of the rectangle.

For the angle in question, the 4.2 cm side is the adjacent leg.

The diagonal of 8.6 cm is the hypotenuse.

The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

`\cos \alpha = (adj)/(hyp)`

`\cos \alpha = (4.2~cm)/(8.6~cm)`

`\alpha = \cos^(-1) (4.2~cm)/(8.6~cm)`

`\alpha = 60.8^\circ`