SOLUTION: <p>Review the following <a rel=nofollow HREF="https://imgur.com/QEVdt2x" target="_blank" rel="noopener">image</a> and solve for <strong>h.</strong></p> <p>Thank you all</p>

Algebra ->  Graphs -> SOLUTION: <p>Review the following <a rel=nofollow HREF="https://imgur.com/QEVdt2x" target="_blank" rel="noopener">image</a> and solve for <strong>h.</strong></p> <p>Thank you all</p>      Log On


   

Question 1103490:

Review the following image and solve for h.


Thank you all
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
image is shown below:

$$$

assign x to the value of the length of the dashed line.

you get:

tan(60) = h/x

tan(30) = h/(x+439)

solve for h in both equations.

you get h = tan(60) * x

you get h = tan(30) * (x + 439)

since they both equal to h, then they are both equal to each other and you get:

tan(60) * x = tan(30) * (x + 439)

simplify to get tan(60) * x = tan(30) * x + tan(30) * 439

subtract tan(30) * x from both sides of the equation to get tan(60) * x - tan(30) * x = tan(30) * 439

factor out the x to get (tan(60) - tan(30)) * x = tan(30) * 439

divide both sides of this equation by (tan(60) - tan(30)) to get x = (tan(30) * 439) / (tan(60) - tan(30))

simplify to get x = 219.5

h = x * tan(60) becomes h = 219.5 * tan(60) which becomes h = 380.1851523.

h = (x + 439) * tan(30) becomes h = (219.5 + 439) * tan(30) which becomes h = 658.5 * tan(30) which becomes h = 380.1851523.

the formula are both in agreement that h = 380.1851523.