Question

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

Answer 1

Answer:

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

Step-by-step 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:

$\beta=arctan(\frac{opposite}{adjacent})$

In this case:

$opposite=6\\\\adjacent=8$

Then:

$\beta=arctan(\frac{6}{8})\\\\\beta=36.86\°$

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

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