Answer:
a. [tex]3.98^{0}[/tex]
b. [tex]1.91mi[/tex]
Explanation:
The data given are
Height,h=550ft,
length of incline plane, L=1.50 miles
first we convert all parameters to meters
since 1ft=0.3048m then 550ft will be 167.76m
also 1mile=1609.34m, hence 1.5mile will be 2414m
From the diagram attached, the length and height formed a simple triangle with the length being the hypotenuse and the height being the opposite.
Hence using SOHCAHTOA, we can conclude that the angle will be
[tex]sin\alpha =\frac{h}{l}\\\alpha=sin^{-1}\frac{167.76}{2414}\\\alpha =3.98^{0}[/tex]
b. the new height becomes
[tex]h=550+150=700ft\\h=0.3048*700=213.36m[/tex]
going by the same formula, we solve the new length s
[tex]sin\alpha =\frac{213.36}{l}\\ l=\frac{213.36}{sin3.98}\\ l=3073.99m\\l=1.91mi[/tex]
