A rectangle is 146cm long. A diagonal makes an angle of 50° with the width. How wide is the rectangle?

w/146 = cot 50°

To find the width of the rectangle, we can use the trigonometric relationship of a right triangle formed by the diagonal and the width of the rectangle.

First, we know that the diagonal is the hypotenuse of the right triangle, and one of the angles formed by the diagonal and the width is 90°. The other angle can be found by subtracting 50° (given in the question) from 90°, since the diagonal makes an angle of 50° with the width.

So, the other angle in the right triangle is 90° - 50° = 40°.

Now, let's denote the width of the rectangle as 'w'. We can use the trigonometric relationship of the right triangle to find the width. Specifically, we can use the tangent function (tan) since we have the opposite side (the width) and the adjacent side (half of the length of the rectangle, since the width bisects the length).

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case, we have:
tan(40°) = w / (146 / 2)

Simplifying this equation, we get:
w = tan(40°) * (146 / 2)

Now we can use a calculator to find the value of tan(40°):
tan(40°) ≈ 0.8391

Plugging in the value of tan(40°) into the equation, we have:
w ≈ 0.8391 * (146 / 2)

Simplifying further, we get:
w ≈ 0.8391 * 73

Finally, calculating w:
w ≈ 61.257

Therefore, the width of the rectangle is approximately 61.257 cm.