What is the height of the hill?

[dcowboys107]

From a point on level ground, an observer measures the angle of elevation to the top of a hill to be 38 degrees The observer then walks 370 meters directly away from the hill and measures the angle of elevation to the top of the hill to be 25 degrees. Determine the height of the hill to the nearest meter.

 

I drew it out and for variables I used "x" as the distance from the first angle measurement to the base of the hill and 370 from the end of the first measurement to the start of the second measurement. I used "h" to represent height. I got cot 38 degrees=x/h and cot 25=(370+x)/h I solved for x in the first equation then plugged it into the second and got finally h=370/(cot 25 - cot 35) why is this answer wrong? Thanks for the help!

[DJBruce]

I am not sure why your method did not work. However whenever I have done this problem I have used Law of Sines to find the hypotenuse of the near triangle and then solved it from their.

[psychlone]

Your equation dcowboys107 from the substitution of equ 1 into equ 2 is correct.

 

[math]\ h = [/math] [math]\frac{370}{cot(25^{\circ})-cot(38^{\circ})}[/math]

 

What you've done is forget to take the reciprocal of tan to equal cot, and then subtracting the two cot’s and divide into 370.

Edited December 13, 2009 by Cap'n Refsmmat
no answers please

[D H]

why is this answer wrong?

 

Three possibilities come to mind:

 

 

Determine the height of the hill to the nearest meter.

1. Did you do what was asked, or did your just paste in the 12 to 16 digit number from your calculator?

 

h=370/(cot 25 - cot 35)

2. What were those two angles again? One of these two (25 and 35 degrees) is inconsistent with the problem as stated.

 

3. And are you calculating cot(25 degrees) or cot(25 radians)?

[mooeypoo]

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