Question

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

To find the height of the canvas, we can use trigonometric functions. Given that the diagonal of the canvas is 23.3 inches and it forms a 31° angle with the bottom of the canvas, we can use the sine function:

\[
\text{Height} = \text{Diagonal} \times \sin(\theta)
\]

Where:
- \(\theta\) is the angle (31°),
- Diagonal = 23.3 inches.

So, we calculate:

\[
\text{Height} = 23.3 \times \sin(31^\circ)
\]

First, we need to find \(\sin(31^\circ)\). Using a calculator:

\(\sin(31°) \approx 0.5150\).

Now, substitute back into the height equation:

\[
\text{Height} = 23.3 \times 0.5150 \approx 12.00 \text{ inches}
\]

Now we round to the nearest inch. Thus, the height of the canvas is approximately **12 inches**.