SOLUTION: The angle of elevation of the top of cell tower B from the top of cell tower A is 30 degrees. The angle of depression of the foot of the cell tower B from the top of cell tower A i

Question 884120: The angle of elevation of the top of cell tower B from the top of cell tower A is 30 degrees. The angle of depression of the foot of the cell tower B from the top of cell tower A is 60 degrees. The height of cell tower B is 100 meters. The foot of cell tower A and the foot of cell tower B is in the same horizontal plane.
What is the height of cell tower A?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the following picture shows the relationship between all the parts.

see below the picture for the analysis.

$$$

tan(30) = a/x

tan(60) = b/x

solve both these equations for x to get:

x = a/tan(30)

x = b/tan(60)

for ease of presentation, let T30 = tan(30) and T60 = tan(60).

because they both equal x, then they are both equal to each other so you get:

a/T30 = b/T60

multiply both sides of this equation by T30 to get:

a = T30/T60 * b

since a + b = 100, you can solve for b to get b = 100 - a.

substitute for b in the equation of a = T30/T60 * b to get:

a = T30/T60 * (100 - a)

simplify this to get:

a = (T30/T60 * 100) - (T30/T60 * a)

add (T30/T60 * a) to both sides of this equation to get:

a + (T30/T60 * a) = (T30/T60 * 100)

factor out the a on the left side of the equation to get:

a * (1 + T30/T60) = (T30/T60 * 100)

divide both sides of this equation by (1 + T30/T60) to get:

a = (T30/T60 * 100) / (1 + T30/T60)

since T30/T670 = 1/3, you can replace T30/T60 with 1/3 and solve for a to get:

a = (1/3 * 100) / (1 + 1/3) which becomes:

a = (1/3 * 100) / (4/3) which becomes:

a = (1/3) * (3/4) * 100 which becomes:

a = 25

since a + b = 100, this means that b = 75 which means that the height of tower A is equal to 75.

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