Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Road Grade

You are driving on a road that has a
6% uphill grade. This means that the slope of the road is
6/100. Approximate the amount of vertical change in your
position when you drive 200 feet.

1. Must I use the distance formula D = rt?

2. Must I use (delta y)/(delta x)?

3. If not, what is the set up here? I will do the math.

Thanks again.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Road Grade

The speed is not a part of this question.  It is just a trigonometry problem.

Be careful about slope questions on roads.  It's a lot easier to calculate the slope using the gain in height (Opp) and the distance along the road (Hyp).  A theodolite will give Opp and there are plenty of ways to find Hyp.

But this question clearly says the slope is 6/100, which means 6 = Opp and 100 = Adj(cent) 

If you drive 200 feet that's a Hyp distance.  So you need to calculate Adj.  6/100 is the tangent not the sine, so you'll have either find the sine or calculate  Adj using Pythag.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Road Grade

The speed is not a part of this question.  It is just a trigonometry problem.

Be careful about slope questions on roads.  It's a lot easier to calculate the slope using the gain in height (Opp) and the distance along the road (Hyp).  A theodolite will give Opp and there are plenty of ways to find Hyp.

But this question clearly says the slope is 6/100, which means 6 = Opp and 100 = Adj(cent) 

If you drive 200 feet that's a Hyp distance.  So you need to calculate Adj.  6/100 is the tangent not the sine, so you'll have either find the sine or calculate  Adj using Pythag.

Bob

How about tan (x) = 6/100?

arctan(tan x) = arctan(6/100)

x = 3.4336303625

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Road Grade

OK. That's the angle of the slope in degrees.

Now use Opp = Hyp x sin(angle)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Road Grade

OK. That's the angle of the slope in degrees.

Now use Opp = Hyp x sin(angle)

Bob

If the set up is 6 = 200 • sin( 3.4336303625), then what variable
am I solving for?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Road Grade

6 isn't that amount.

Imagine a triangle ABC with a right angle at B and angle A = 3.43 degrees.  So BC = 6 and AC = 100.

Now a second, larger triangle DEF with a right angle at E and angle D = 3.43 degrees.  DF = 200 and you are trying to find EF.

So EF = 200 * sine(3.43)

That isn't 6.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Road Grade

6 isn't that amount.

Imagine a triangle ABC with a right angle at B and angle A = 3.43 degrees.  So BC = 6 and AC = 100.

Now a second, larger triangle DEF with a right angle at E and angle D = 3.43 degrees.  DF = 200 and you are trying to find EF.

So EF = 200 * sine(3.43)

That isn't 6.

Bob

Ok. My set up is wrong. It now makes sense.