Question

A water tower is located 354 feet from a building. From a window in the building, an observer notes that the angle of elevation to the top of the tower is 42° and that the angle of depression to the bottom of the tower is 20°.


How tall is the tower?

How high is the window from the ground?

Answer 1

An isosceles triangle has an area of 24 yd², and the angle between the two equal sides is 166°. Find the length of the two equal sides.

Answer 2

It's easier to solve if you draw the figure. If you're not sure what 'angle of elevation' or 'angle of depression' is about, I suggest you read some lectures about it first.

In your drawing, you can separate them into two right triangles.
One triangle has an angle of 20°, with a height of 354 feet. We can solve for its base using tangents:
tan(angle) = opposite / adjacent
tan(20°) = a / 354
354*tan(20°) = a
a = 128.85 ft

The other triangle has an angle of 42°, with height of 354 feet. We can also solve for its base using tangents:
tan(angle) = opposite / adjacent
tan(42°) = b / 354
354*tan(42°) = b
b = 318.74 ft

The height of window is equal to a.
To get the height of tower, get the sum of a and b: a + b = ?

Hope this helps~ `u`