A 90-ft pole casts a shadow as shown in the figure.

(a) Express the angle of elevation of the sun as a function of the length s of the shadow.

(a)

The angle of elevation is the angle between the horizontal and the line from the object to the observers eye.

The height of the tree is 90 ft.

Let the length of the shadow be $\"\"$ ft.

Draw the diagram of the situation:

$\"\"$

Angle of elevation is $\"\"$

(b)

The length of the shadow is 35 ft.

From (a): Angle of elevation is $\"\"$

$\"\"$

Angle of elevation is $\"\"$ .