I'm guessing that the two expressions are for separate equilateral triangles.
If so, the equations would be:
3(3x-14)=180
3(x+4)=180
to solve the first equation, divide by 3:
3x-14=60
then, add 14 to both sides:
3x=74
lastly, divide both sides by 3:
x=24.667
to solve the second equation, divide both sides by 3:
x+4=60
then, subtract 4 from both sides:
x=56
keeping in mind that in a parallelogram the diagonals bisect each other, namely cut each other into two equal halves. Check the picture below.
![\stackrel{GH}{3x-4}~~ = ~~\stackrel{HE}{5y+1}\implies 3x=5y+5\implies x=\cfrac{5y+5}{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{DH}{x+1}~~ = ~~\stackrel{HF}{3y}\implies \stackrel{\textit{substituting "x" in the equation}}{\cfrac{5y+5}{3}+1~~ = ~~3y}](https://tex.z-dn.net/?f=%5Cstackrel%7BGH%7D%7B3x-4%7D~~%20%3D%20~~%5Cstackrel%7BHE%7D%7B5y%2B1%7D%5Cimplies%203x%3D5y%2B5%5Cimplies%20x%3D%5Ccfrac%7B5y%2B5%7D%7B3%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7BDH%7D%7Bx%2B1%7D~~%20%3D%20~~%5Cstackrel%7BHF%7D%7B3y%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bsubstituting%20%22x%22%20in%20the%20equation%7D%7D%7B%5Ccfrac%7B5y%2B5%7D%7B3%7D%2B1~~%20%3D%20~~3y%7D)
Complete Question
The length of the guy wire supporting a cell tower is 120 m. The guy wire is anchored to the ground at a distance of 80 m from the base of the tower to the nearest hundredth of a meter how tall is the tower?
Answer:
89.44m
Step-by-step explanation:
We solve this question using the Pythagoras Theorem
This is given as:
Hypotenuse² = Opposite ² + Adjacent ²
Hypotenuse = Length of the guy wire = 120m
Adjacent = Distance from the base of the tower = 80m
Opposite = Height of the building = x
Hence:
120² = x² + 80²
Collect like terms
x² = 120² - 80²
x = √120² - 80²
x = √(8000)
x = 89.4427191 m
Approximately the height of the tower is = 89.44m
