SOLUTION: This is Applications of Trigonometry, that involves the law of sines. I can't figure out the diagram. After that I would know what to do. A huge mound of dirt is near a construc

Question 957691: This is Applications of Trigonometry, that involves the law of sines. I can't figure out the diagram. After that I would know what to do.
A huge mound of dirt is near a construction site. Andrew wants to find out how high the mound is. He measures the angle to the top of the mound to be 57 degrees. Then he walks 8 feet away from the base of the mound and measures the angle to the top of the mound again to be 35 degrees. To the nearest tenth of a foot, what is the height of the mound?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your diagram is shown below:

$$$

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 =

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 = 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.

RELATED QUESTIONS
i need the proof of law of cosines and... (answered by AnlytcPhil)

what is the law of... (answered by checkley71)

I need help understanding how to figure out a problem using the law of sines using only... (answered by solver91311)

Answer the following accordingly. 1.state the law of sines. 2.in which cases,can we use (answered by josgarithmetic)

When would you use the law of sines? (answered by amarjeeth123)

Describe, in detail, when to use the law of cosines, the law of sines, and the law of... (answered by Edwin McCravy)

In the following exercise, solve the triangle for the remaining sides and angles. A=46 (answered by Alan3354)

Greetings, I am in Trig but i am struggling with old knowledge, Heres the Problem: (answered by mananth)

This is driving me crazy. I finally solved my problem, but I can�t figure out why my... (answered by kensson,MathTherapy)