Question

A hummingbird is flying toward a large tree that has a radius of 6 feet. When it is 33 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?

Answer 1

Answer:

Length of the arc = 5.25017 feet

Step-by-step explanation:

The line from the middle of the tree to the tip of the tangent lines is 33 ft and from the circumference of the tree its 27ft. One of the right angle triangles is picked and the angle is determined using SOHCAHTOA

Hence Tan X = 6/27

X = Tan-1 (6/27) = 12.52880770915o

Hence both sum of angles where tangent lines meet = 2 x 12.52880770915o = 25.05761541830o

Angle of the arc inside the circle = 50.115o

Length of the arc = 50.115/360 x (2x22/7 x 6) = 5.25017040025ft