Question

If a road has a grade of 30°, this means that it's angle of elevation is 30°. If you travel 1.5 miles on this road, how much elevation have you gained in feet (5280ft = 1 mile). Round to the nearest foot.

Answer 1

3960ft

Explanation:

The elevation gained after traveling 1.5 miles will be 3960ft.

Explanation:

Angle of elevation = 30°

Distance travelled= 1.5 miles

1 mile = 5280 ft.

1.5 miles = 5280 x 1.5

= 7920 ft.

The height from the ground can be calculated by,

sin 30° = height / 7920

1/2 = height / 7920

Height = 7920/2

= 3960 ft.

The elevation gained after traveling 1.5 miles will be 3960ft.

Answer 2

`3,960\ ft`

Explanation:

we know that

Applying trigonometric identity

`sin(30^o)=(y)/(1.5)` ---> by SOH (opposite side divided by the hypotenuse)

where

y is the elevation

solve for y

`y=(1/2)1.5=0.75\ miles`

Convert miles to feet

Remember that

`5,280\ ft = 1\ mile`

so

`0.75\ miles=0.75(5,280)=3,960\ ft`