How Tall is the Tower in This Classic 1957 Math Problem?

[Tompson Lee]

Here is a problem I found which is from a math class in 1957:

A man is standing due East of a tower and notes it subtends an angles of 45 degrees with the tower.
He walks South 42.4 feet and the subtended angle is 30 degrees.
How tall is the tower?

(You are only allowed to use only pencils(pens) and papers)

 

[jedishrfu]

Did you draw a diagram of it?

If you consider east to be the x-axis then the man is x feet from the tower and when he looks up it’s at an angle of 45 degrees. How tall is the tower in x feet?

Next consider south to be the y-axis then he walks 42 feet south which takes him further from the tower and looks up it’s now only 30 degrees.

The first part describes a 45-45-90 degree right triangle and the second part describes a 30-60-90 degree right triangle.

Both triangles share a common side, what is it?

Draw a diagram and use your knowledge of these triangles to get the height.

Where did you find this problem?