Ahummingbird is flying toward a large tree that has a radius of 5 feet. when it is 32 feet from the center of the tree, its lines of sight form two tangents. what is the measure of the arc on the tree that the hummingbird can see?

We illustrate this problem by drawing two radii (5 feet) that are each perpendicular to each tangent lines (the line of sight of the hummingbird). We then draw a line connecting the center of the circle and the hummingbird which measures 32 feet. The resulting figure is two right triangles, with 32 as its hypotenuse and 5 as its base. We then find the angle between 5 and 32. 

To find the angle, we find arccos(5/32) = 81.01°.
Multiplying by 2 since there are two angles formed:
2 x 81.01° = 162.0°
This is the measure of the arc on the tree which the hummingbird can see.