SOLUTION: 3) To find the height of a tower, a surveyor positions a measurement device that is 2 m tall at a spot 24 m from the base of the tower. She measures the angle from the top of the m

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Question 1199540: 3) To find the height of a tower, a surveyor positions a measurement device that is 2 m tall at a spot 24 m from the base of the tower. She measures the angle from the top of the measurement device to the top tower to be 45°. What is the height of the tower? Show your work.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Diagram:


Segments:
AB = CD = 24 meters
AD = BC = 2 meters
CE = h = unknown (in meters)

Angle:
Angle CDE = 45 degrees

Triangle CDE is a right triangle.
Furthermore, it is a 45-45-90 triangle which makes it isosceles.
The two legs CD and CE are congruent. Both are 24 meters long.
Therefore, h = 24.

Alternatively, you can use the tangent function to go from
tan(45) = h/24
to
h = 24

tan(45) = 1 when in degree mode.

The total height of the tower is: BC+CE = 2+24 = 26 meters

Side note: 26 meters = 85.3018 feet approximately.