Question 957691
your diagram is shown below:


<img src = "http://theo.x10hosting.com/2015/032303.jpg" alt="$$$" </>


the height of your mound is h.
the distance between the center of the mound and the 57 degree angle is x.
the distance between the center of the mound and the 35 degree angle is x + 8.


tan(57) = h/x


tan(35) = h/(x+8)


solve for x in these equations to get:


x = h / tan(57)


x = h / tan(35) - 8


replace x with h / tan(57) in the second equation to get:


h / tan(57) = h / tan(35) - 8


solve for h in this equation to get h = {{{(-8 * tan(35) * tan(57)) / (tan(35) - tan(57))}}}


i'm assuming you know how to solve for h in that equation.
if you don't, let me know and i'll step you through it.


the equation of h = {{{(-8 * tan(35) * tan(57)) / (tan(35) - tan(57))}}} gets you h = 10.27299966.


now that you know h, you can solve for x.


tan(57) = h/x is the equation you start with.


solve for x in this equation to get x = h / tan(57).


use the value of h you just solved for to get x = 10.27299966 / tan(57) which results in x = 6.671363981.


you can now confirm that your answer for h is correct.


tan(57) = h/x becomes tan(57) = 10.27299966 / 6.671363981 which becomes tan(57) = 1.539864964.


use your calculator to find tan(57) = 1.539864964.


since they're the same, your value of h and x is good for tan(57).


x + 8 is equal to 6.671363981 + 8 which is equal to 14.671363981.


tan(35) = h / (x+8) becomes tan(35) = 10.27299966 / 14.671363981 which becomes tan(35) = .7002075382.


use your calculator to find tan(35) = .7002075382.


since they're the same, your value of h and (x+8) is good for tan(35).


the height of your mound is 10.27299966 feet which rounds to 10.3 feet.