Word Problem

Question

The grade of a highway up a hill is 30%. How much change in horizontal distance is there if the vertical height of the hill is 435 feet? Express the answer to the nearest foot.

Answer 1

Ok I can't draw this but it is a right triangle trig problem.  You have a triangle with an angle of 30 degrees and the hypotenuse is 435 and you need the length of the base leg.

 

you know the soh cah toa rules and in this case your equation is 

 

cos 30 deg = x / 435

 

You should know your 30/60/90 triangle and its trig functions on the unit circle by heart or at least be able to derive them!  The cos of 30 degrees is rad 3/ 2 so your equation is

 

rad 3/2  * 435 = x

 

x = 377 (rounded)

 

 

All the best 

 

Lori