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#1 2021-05-05 12:48:49

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.

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#2 2021-05-05 19:33:07

Bob
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Registered: 2010-06-20
Posts: 10,058

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 smile

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#3 2021-05-05 19:46:54

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Road Grade

Bob wrote:

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

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#4 2021-05-05 19:54:02

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

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 smile

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#5 2021-05-05 20:08:52

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Road Grade

Bob wrote:

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?

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#6 2021-05-05 20:33:18

Bob
Administrator
Registered: 2010-06-20
Posts: 10,058

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 smile

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#7 2021-05-06 10:47:16

mathland
Member
Registered: 2021-03-25
Posts: 444

Re: Road Grade

Bob wrote:

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.

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