Answer:
The ramp should be 32.9 feet longer.
Step-by-step explanation:
When the ramp is at [tex]6^{o}[/tex] to the ground, its length can be determined by applying the appropriate trigonometric function. Let the length be represented by l, so that;
Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin [tex]6^{o}[/tex] = [tex]\frac{3.45}{l}[/tex]
l = [tex]\frac{3.45}{Sin 6^{o} }[/tex]
= [tex]\frac{3.45}{0.10453}[/tex]
= 33.0048
l = 33.0 feet
When the angle is reduced to [tex]3^{o}[/tex], the length of the ramp would be;
Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin [tex]3^{o}[/tex] = [tex]\frac{3.45}{l}[/tex]
l = [tex]\frac{3.45}{Sin 3^{o} }[/tex]
= [tex]\frac{3.45}{0.05234}[/tex]
= 65.9152
l = 65.9 feet
Change in length of ramp = 65.9 - 33.0
= 32.9
The ramp should be 32.9 feet longer.
