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

Answer:

$3,960\ ft$

Step-by-step explanation:

we know that

Applying trigonometric identity

$sin(30^o)=\frac{y}{1.5}$ ---> 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

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