Triangles- Story Math Problem I can't figure it out..!!

[Katie_Marie]

The question is:


John wants to measure the width of a stream using the methods he has learned in geometry. He puts a stake in the ground oppsite a big tree. The steps John would use to find the measure he wants are given below in random order. Put the number next to the following statements to indicate the proper sequence John would use to find the measure he wants.

1. John drives a second stake in the ground
2. John meaures the distance between the two stakes.
3. John multipiles the distance between the two stakes by 1.7 to find the distance.
4. John uses a compass to walk away from the stake at a right angle.
5. John drives a stake opposite the tree to establish a line between two points
6. On the path john walks until he finds a like of sight to the tree that equals 60 degrees.

I need help putting that in the correct order. Please I've been working on it for 2 days!!

 

[Loren]

Did you draw a sketch and note the steps you took to arrive at the result? The idea seems to be to construct a 30-60 degree right triangle where the side of the stream that you are on is the small leg of the triangle. The long leg is the side of the triangle between the tree and the first stake. The hypotenuse is between the tree and the second stake. The second driven stake is at the vertex of the 60 degree angle. The 1.7 is a little misleading because the true measure would be square root of 3 or 1.732.
Hope this helps.

 

[Maccrea99]

Did you draw a sketch and note the steps you took to arrive at the result? The idea seems to be to construct a 30-60 degree right triangle where the side of the stream that you are on is the small leg of the triangle. The long leg is the side of the triangle between the tree and the first stake. The hypotenuse is between the tree and the second stake. The second driven stake is at the vertex of the 60 degree angle. The 1.7 is a little misleading because the true measure would be square root of 3 or 1.732.
Hope this helps.

So would the 1.7 be the last number?

 

[Deleted member 4993]

So would the 1.7 be the last number?.......................... NO!!

This is a 5⁺ year old thread - why are you resurrecting it?

 

[Maccrea99]

1.7 was the last number and because I needed help, why does it matter?

 

[Deleted member 4993]

1.7 was the last number and because I needed help, why does it matter?

Did you read the original question? What did it ask for?

 

[HallsofIvy]

1.7 was the last number and because I needed help, why does it matter?

If you want help then it would be better to start a new thread and state exactly what help you want. Asking "would 1.7 be the last number" means nothing to me. What do you mean by "the last number"? And what, exactly is your question? Is your exercise identical to this problem?

 

[HallsofIvy]

The question is:


John wants to measure the width of a stream using the methods he has learned in geometry. He puts a stake in the ground oppsite a big tree. The steps John would use to find the measure he wants are given below in random order. Put the number next to the following statements to indicate the proper sequence John would use to find the measure he wants.

1. John drives a second stake in the ground
2. John meaures the distance between the two stakes.
3. John multipiles the distance between the two stakes by 1.7 to find the distance.
4. John uses a compass to walk away from the stake at a right angle.
5. John drives a stake opposite the tree to establish a line between two points
6. On the path john walks until he finds a like of sight to the tree that equals 60 degrees.

I need help putting that in the correct order. Please I've been working on it for 2 days!!

Since this has been resurrected, the problem starts by saying "John wants to measure the width of a stream using the methods he has learned in geometry. He puts a stake in the ground opposite a big tree." Obviously his first step is "5. John drives a stake opposite the tree to establish a line between two points". There really isn't much "mathematics" required here- just common sense.

Now look at the others to decide which should be next:
"1. John drives a second stake in the ground". Why would he drive a second stake right next to the first?
"2. John measures the distance between the two stakes". At this point you have only one stake so this makes no sense!
"3. John multiplies the distance between the two stakes by 1.7 to find the distance". Same objection as before- you do not have two stakes!
"4. John uses a compass to walk away from the stake at a right angle". Okay, that's certainly something that is possible.
"6. On the path John walks until he finds a line of sight to the tree that equals 60 degrees". The problem I have with this is that there is no "path" mentioned before. I suspect they mean that John walks along the line at right angles from (4.)

Okay so far, the only things that seem possible are 5, 4, 6, in that order. John has now placed a stake marking a line from the stake to the tree.

Now, it makes sense for John to drive a second stake, (1.) We have 5, 4, 6, and 1. Left are only 2 and 3. He cannot "multiply the distance between the two stakes by 1.7" until he has measured that distance! So it must end with 2 and then 3.

Mathematically John recognizes that the ratio of "opposite side" to "near side" in a right triangle with angle 60 degrees is $\displaystyle tan(60)= \sqrt{3}{2}$ which is approximately 1.7. But you don't need to know that or know anything about trigonometry to answer the question!