Three students were asked to draw a diagram of the following situation and their responses are recorded below: A 6-foot tall man is standing 20 feet from a flagpole when he notices a puddle between him and the flagpole. The man can see the top of the flagpole in the center of the puddle. If the puddle is four feet away from the man, how tall is the flagpole?

Which student correctly drew the diagram and what is the height of the flagpole?

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Angle of Depression and Angle of Elevation

One application of the trigonometric ratios is to find lengths that you cannot measure. Very frequently, angles of depression and elevation are used in these types of problems.

Angle of Depression: The angle measured down from the horizon or a horizontal line.

Angle of Elevation: The angle measured up from the horizon or a horizontal line.

What if you placed a ladder 10 feet from a haymow whose floor is 20 feet from the ground? How tall would the ladder need to be to reach the haymow's floor if it forms a 30∘ angle with the ground?

x is variable or an unknown value to find

example:

2x = 5 which means x = 3