Question

A parallelogram has sides of length `15.4` and `9.8`. Its area is `72.9`. Find the measures of the angles?

Thanks in advance

Answer 1

The acute angles are `28.8°` and the obtuse angles are `151.1°`

Explanation:

If you have one of the sides (let's call it the base) and the area, then you can find the height of the parallelogram. (The perpendicular distance between the two sides,)

`h = A/b = 72.9/15.4`

This leads to a most uncomfortable decimal, so I opted to work with fractions for the sake of accuracy.

`72.9/15.4 = 729/154 = 4 113/154`

You can now draw a right-angled triangle in the parallelogram.

The hypotenuse is the shorter side of the parallelogram `(9.8)` and the perpendicular height (the side opposite the smaller angle) is the value we have just calculated.

From the opposite side and the hypotenuse, we can calculate the sin of the angle:

`sin theta = (4 113/154)/15.4 = 0.4830`

`theta = 28.9°" "larr` the acute angles of the parallelogram.

The obtuse angles of the parallelogram will be the supplement of `28.9°`

`180°-28.9° = 151.1°`