Question

You are driving up a long, inclined road. After 1.50 mi you notice that signs along the roadside indicate that your elevation has increased by 550 ft
a) What is the angle of the road above the horizontal?
b) How far do you have to drive to gain an additional 150ft of elevation?

Answer 1

Answer:

a. 3.98^{0}

b. 1.91mi

Explanation:

I took the test

Answer 2

Answer:

a. $3.98^{0}$

b. $1.91mi$

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

$sin\alpha =\frac{h}{l}\\\alpha=sin^{-1}\frac{167.76}{2414}\\\alpha =3.98^{0}$

b.  the new height becomes

$h=550+150=700ft\\h=0.3048*700=213.36m$

going by the same formula, we solve the new length s

$sin\alpha =\frac{213.36}{l}\\ l=\frac{213.36}{sin3.98}\\ l=3073.99m\\l=1.91mi$