Question 1207377
angle A is equal to 45 degrees 30 minutes = 45 + 30/60 = 45.5 degrees.
angle B is equal to 44 degrees 10 minutes = 44 + 10/60 = 44.16666... degrees.


two triangle are formed with a common vertical side of h.
the angle closest to h is angle A.
the angle farthest to h is angle B.
angle A has an adjacent side of x and an opposite side of h.
angle B has an adjacent side of x + 39 and an opposite side of h.


you have tan(A) = h/x and you have tan(B) = h / (x + 39).


solve for h in both of those equations to get h = x * tan(A) and h = (x + 39) * tan(B).


simplify to get h = x * tan(A) and h = x * tan(B) + 39 * tan(B)


since h = h, then x * tan(A) = x * tan(B) + 39 * tan(B)


subtract x * tan(B) from both sides of the equation and factor out the x to get x * (tan(A) - tan(B)) = 39 * tan(B)


divide both sides of the equation by (tan(A) - tan(B)) to get x = 39 * tan(B) / (tan(A) - tan(B))


since A = 45.5 degrees and B = 44.166666..... degrees, you get x = 39 * tan(44.166666...) / (tan(45.5 - tan(44.166666...) = 818.5122291.


that's how far point A is from the base of the antenna.


i confirmed the value of x was correct, because:


h = tan(A) * x = tan(45.5) * 818.5122291 = 832.9240955 and .....
h = tan(B) * (x + 39) = tan(44.16666...) * 857.5122291 = 832.9240955.
they're the same value as they should be.


here's my diagram.


<img src = "http://theo.x10hosting.com/2024/053001.jpg">


i used storage of ti-84 plus to hold the values.
those storage locations are A, B, C, D, E, and F indicated by ----> .....


let me know if you have any questions.
theo