Question

You are driving up a long, inclined road. After 1.40 mi you notice that signs along the roadside indicate that your elevation has increased by 530 ft . You may want to review (Pages 62 - 65) .

What is the angle of the road above the horizontal?

How far do you have to drive to gain an additional 130 ft of elevation?

Answer 1

Part A.

In a right-angle triangle,

distance traveled by you along the incline = Hypotenuse = 1.40 mi

(Since 1 mile = 5280 ft), So

Hypotenuse = 1.40 mi = 1.40*5280 ft = 7392 ft

Vertical elevation of car = perpendicular = 530 ft

So, angle of road above the horizontal '' will be:

sin = Perpendicular/Hypotenuse = 530/7392

= arcsin (530/7392) = 4.11 deg

Part B.

When new vertical elevation is = perpendicular = 530 ft + 130 ft = 660 ft

then hypotenuse for same road will be:

sin = perpendicular/hypotenuse

hypotenuse = perpendicular/sin = 660/sin 4.11 deg = 9209 ft

Additional distance which needs to be driven by you = 9209 - 7392 = 1817 ft

Since 1 mi = 5280 ft, So

Additional distance which needs to be driven by you = 1817 ft = (1817 ft)*(1 mi/5280 ft) = 0.344 mile