Question

A rectangle measures 6 m by 8m. find the acute angle at which the diagonals intersect

Answer 1

The acute angle at which the diagonals intersect is:
`73.72\°`

Explanation:

An acute angle is an angle that measures less than 90 degrees.

Observe the rectangle attached, where
`\alpha` is the acute angle at which the diagonals intersect.

First, you need to find the measure of the angle β.

In order to find β, use this inverse trigonometric function:

`\beta=arctan((opposite)/(adjacent))`

In this case:

`opposite=6\\\\adjacent=8`

Then:

`\beta=arctan((6)/(8))\\\\\beta=36.86\°`

The angle
`\alpha` is twice the angle
`\beta`. Then, this is:

`\alpha =2\beta\\\\\alpha=2(36.86\°)\\\\\alpha=73.72\°`