The length of ramp is 8.9 meters approximately.
Given that, the entrance of the old town library is 2.3 feet above ground level.
A ramp from the ground level to the library entrance is scheduled to be built.
The angle of elevation from the base of the ramp to its top is to be 15º
We have to find the length of the ramp.
Let the length of ramp be “n” feet.
Now, if we observe there forms a right angle triangle with ramp as hypotenuse and height of entrance as opposite side for angle of elevation 15 degrees.
The diagram is attached below
In the figure,
AC = length of ramp
AB = height above ground level = 2.3 feet
angle of elevation = 15 degree
Then, we know that,
[tex]\sin \theta=\frac{\text {opposite side}}{\text {hypotenuse}}[/tex]
where θ is angle of elevation.
[tex]\begin{array}{l}{\sin 15^{\circ}=\frac{2.3 \text { feet }}{n \text { feet }}} \\\\ {\rightarrow 0.2588=\frac{2.3}{n}} \\\\ {\rightarrow n=\frac{2.3}{0.2588}} \\\\ {\rightarrow n=8.8865}\end{array}[/tex]
Hence, the length of the ramp is 8.9 meters approximately.
