Isabella is making a huge flag of her country, the Republic of Seychelles, on a canvas
\[20\] by
\[10\] meters long.
To do that, she has to draw a diagonal that begins at the bottom-left corner and ends at the right side of the flag, at a height of
\[7\] meters.
Since the ends of the diagonal are too far to put a ruler between them, Isabella wanted to find the angle of the diagonal and draw it using a protractor.
What is the angle of elevation, in degrees, of the diagonal?
Round your final answer to the nearest tenth.

Isabella is making a flag that is 20 meters wide and 7 meters high. We need to find the angle of elevation of the diagonal from the bottom-left corner to the right side of the flag. To do this, we can use the tangent trigonometry operation.

Solving:

[tex]\subsection*{The Triangle:}\begin{itemize} \item The base (horizontal distance) is $ d = 20 $ meters. \item The height (vertical distance) is $ h = 7 $ meters.\end{itemize}[/tex]

[tex]\subsection*{Tangent Function:}The tangent of the angle of elevation $ \theta $ is given by the ratio of the opposite side (height) to the adjacent side (base):\[\tan(\theta) = \frac{h}{d} = \frac{7}{20}\][/tex]

[tex]\subsection*{Find the Angle:}To find the angle $ \theta $, we use the arctangent(inverse tangent) function:\[\theta = \tan^{-1}\left(\frac{7}{20}\right)\][/tex]

[tex]\subsection*{Use a Calculator:}\[\theta \approx \tan^{-1}(0.35) \approx \boxed{19.3^\circ}\][/tex]

Therefore, the angle of elevation of the diagonal is 19.3 degrees.