Question
Louie is trying to find a rectangular canvas for his art project. Its height must measure 18 inches and form a
12 inches
14 inches
24 inches
27 inches
12 inches
14 inches
24 inches
27 inches
Ask by Griffiths Rojas. in the United States
Jan 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The diagonal of the canvas is approximately 24 inches.
Solution
To find the length of the diagonal of the canvas, we can use trigonometric relationships. Given that the height of the canvas is
The sine of an angle in a right triangle is defined as the ratio of the opposite side to the hypotenuse. In this case, the height of the canvas is the opposite side, and the diagonal is the hypotenuse.
The relationship can be expressed as:
Where:
-
-
inches -
is the length of the diagonal.
Rearranging the formula to solve for
Now, we can substitute the known values into the equation:
Let’s calculate
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Calculate the trigonometric value:
Calculating the diagonal gives us:
Since the options provided are 12 inches, 14 inches, 24 inches, and 27 inches, the closest match to our calculated diagonal length is 24 inches.
Thus, the length of the diagonal of the canvas is approximately 24 inches.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To find the length of the diagonal of the canvas, we can use basic trigonometry. Given that the height
Solving this for
So, the diagonal is closest to 24 inches.
Now, let’s take a moment to appreciate that trigonometry not only helps in solving geometry problems but also has real-world applications! Whether it’s constructing buildings, creating art, or designing video game graphics, the relationships between angles and sides are vital for accuracy and creativity!
