Question

For each problem read the question at least twice before drawing a large clear diagram.

A rectangle is 100 meters long and 50 meters wide. Find the acute angle between the diagonals.
A) 26 degrees
B) 64 degrees
C) 90 degrees
D) 180 degrees

Answer 1

To find the acute angle between the diagonals of a rectangle, we can use trigonometry to find the measure of one of the angles in the rectangle. Using the given dimensions of the rectangle and the tangent function, we can calculate that the angle is approximately 26 degrees.

Step-by-step explanation:

To find the acute angle between the diagonals of a rectangle, we need to first find the measure of one of the angles in the rectangle. Since we are given the length and width of the rectangle, we can use trigonometry to find this angle.

Consider one of the right triangles formed by the diagonals of the rectangle. The base of the triangle is half the width of the rectangle, and the height is half the length of the rectangle. Using the tangent function, we can find the measure of the angle as follows:

tan(angle) = (half the width)/(half the length)

Substituting the given values, we have:

tan(angle) = (50/2)/(100/2)

tan(angle) = 0.5

Taking the inverse tangent of both sides, we get:

angle = arctan(0.5)

Using a calculator, we find that the angle is approximately 26 degrees. Therefore, the correct answer is (A) 26 degrees.