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?
How tall is the tower?
How high is the window from the ground?
Answers
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.
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`
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`