a rectangle is 17 inches wide 29 inches long what angle does the diagonal make with the lengths?

tan theta = 17/29

Hey, draw a sketch for these problems so you can see what is opposite, what is adjacent and what is hypotenuse.

To find the angle the diagonal makes with the lengths of a rectangle, we can use trigonometry.

First, let's find the length of the diagonal using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides.

In our case, the two sides are the width and the length of the rectangle. Let's call the width "a" and the length "b". Using the formula:

diagonal^2 = width^2 + length^2

diagonal^2 = 17^2 + 29^2
diagonal^2 = 289 + 841
diagonal^2 = 1130

Taking the square root on both sides, we get:

diagonal = sqrt(1130)
diagonal ≈ 33.63 inches

Now, let's find the angle. In this case, we have a right triangle, and the angle we're interested in is between the diagonal and the length of the rectangle. Let's call this angle "θ".

To find θ, we can use the inverse trigonometric function "arctan" (also denoted as tan^(-1)). Applying arctan to the ratio of the length to the width:

θ = arctan(length / width)
θ = arctan(29 / 17)
θ ≈ 59.06 degrees

Therefore, the angle the diagonal makes with the lengths of the rectangle is approximately 59.06 degrees.