Answer:
The ramp is 32.7 feet long
Step-by-step explanation:
The geometrical conditions of the question are shown in the figure below.
Let L be the length of the ramp. The ramp, the wall of the building, and the ground form a right triangle where L is its hypotenuse and the distance of 32 ft is the adjacent leg to the angle of 12°.
To find the length of the hypotenuse, we use the trigonometric ratio called the cosine:
[tex]\displaystyle \cos\beta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \cos12^\circ=\frac{32}{L}[/tex]
To find L, we solve the above equation:
[tex]\displaystyle L=\frac{32}{\cos12^\circ}[/tex]
The cosine of 12° is computed with a scientific calculator:
[tex]\displaystyle L=\frac{32}{0.978}[/tex]
L = 32.7 feet
The ramp is 32.7 feet long
