Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a 31° angle with the bottom of the canvas. What is the height of the canvas? Round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches

A rectangle has right angles as its interior angles. Secondly, when you draw a diagonal and has its angle with bottom, then you get a right angled triangle with known angle.
The height of the rectangle is  given by:

Option D: 12 inches

The height of that rectangular canvas.

I have attached a figure below which you can refer.

The triangle ABC is right angled  triangle. Using the sine ratio from angle A's viewpoint:

Thus, the height of the specified canvas is 12 inches.

Thus, Option D: 12 inches is correct.

Learn more about sine ratio here:

link

12 inches

Step-by-step explanation:

Given

Required

Determine the height of the canvas

The question is illustrated using the attached image.

Using the attachment as a point of reference, the height is calculated from

This gives:

Make h the subject

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

$452.90 because you needed to round to the nearest cent