SOLUTION: Hello, I tried the following formula and the online tool is stating that my answer is wrong. What did I do wrong? Thank you The problem states: You have a special survey tool th

Algebra ->  Triangles -> SOLUTION: Hello, I tried the following formula and the online tool is stating that my answer is wrong. What did I do wrong? Thank you The problem states: You have a special survey tool th      Log On


   

Question 920750: Hello, I tried the following formula and the online tool is stating that my answer is wrong. What did I do wrong?
Thank you
The problem states:
You have a special survey tool that lets you look up at objects at a 30 degree angle relative to the ground. You place the object on the ground in such a way that the nearby top of a tree appears in the viewfinder. If the distance from the tool to the bottom of the tree measures 14.7 feet. What is the height of the tree in feet?
I did the following steps:
14.7/x= Radical 3 over 1
X times Radical 3=14.7
X=14.7 divided by radical 3
X= 14.7 times radical 3 / radical 3 times radical 3
X=14.7 times radical 3 / 3
assuming radical 3 is equal to 1.7
then, X=14.7 times 1.7 / 3
or X=8.33
Why is my answer wrong?
Thanks
Found 3 solutions by josgarithmetic, VishalSE, KMST:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You have a distance on the ground, 14.7 feet, and an acute angle at the ground of 30 degrees. You can use TANGENT of 30 degrees.

Let y be the height of tree from ground to top.
y%2F14.7=tan%2830%29
You wanted to step using radians, so tan%28pi%2F6%29=%281%2F2%29%2F%28sqrt%283%29%2F2%29=1%2Fsqrt%283%29, and you can use it in this form.
y=14.7%2Atan%28pi%2F6%29
y=%2814.7%29%281%2Fsqrt%283%29%29
Rationalize the denominator if you want...
highlight%28y=%2814.7%29%2Asqrt%283%29%2F3%29

Answer by VishalSE(2) About Me  (Show Source):
You can put this solution on YOUR website!
You can use trigonometry as given in above ans. If you have again any problem, you can ask..

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Maybe the online tool expected 4.9sqrt(3) for an answer,
because 14.7%2Asqrt%283%29%2F3=%2814.7%2F3%29%2Asqrt%283%29=4.9sqrt%283%29 .

Maybe it expected 8.487 or 8.49 or 8.48 .
Your rounding of sqrt%283%29=1.732060808 to 1.7 is a bit extreme.
If you are given 14.7 as a piece of data, with 3 significant digits,
your rounding should be at least as accurate.

I would use sqrt%283%29=1.73 or sqrt%283%29=1.732 .
4.9%2A1.73=8.477 rounds to 8.48
4.9%2A1.732=8.4868 rounds to 8.49 or 8.487

Better yet, you could use a calculator, getting 8.487048957 as a result, and only round at the end, to 8.49 or 8.487 .

NOTE:
In science, you round single final results to match the accuracy of the data,
and you keep more digits for intermediate results,
or (in some cases) final results that are measurements for elements of a group when you are trying to show/measure variability.