Question

30 POINTS!!! 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

Answer 1

Answer:

12 inches

Step-by-step explanation:

Given

$\theta = 31^{\circ}$

$diagonal = 23.3\ in$

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

$sin \theta = \frac{opp}{hyp}$

This gives:

$sin 31^{\circ}= \frac{h}{23.3}$

Make h the subject

$h = 23.3 * sin(31^{\circ)$

$h = 23.3 * 0.5150$

$h = 11.9995$

$h = 12\ inches$

Answer 2

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

Given that:

• There is a rectangular canvas.
• The angle that the diagonal of the rectangle makes with bottom  is 31°
• The length of diagonal = 23.3 inches

To find:

The height of that rectangular canvas.

Using the right angle triangle and sine ratio to find height of 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:

$sin(A) = \dfrac{BC}{AC}\\\\ sin(31^\circ) = \dfrac{h}{23.3}\\\\ h \approx 0.515 \times 23.3\\ h \approx 12 \: \rm inches$

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

Thus, Option D: 12 inches is correct.

Learn more about sine ratio here:

https://brainly.com/question/520591