From the top of a tree, a bird looks down on a field mouse at an angle of depression of 50°. if the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes. round the answer to the nearest tenth. a. 33.6 m b. 42.0 m c. 47.7 m d. 59.6 m select the best answer from the choices provided

c. 47.7 m

Step-by-step explanation:

If you draw a right triangle to represent the problem, the catheti are the vertical distance from the bird's eyes to the field mouse and the separation from the field mouse to the base of the tree. The  50° of depression is measured from the horizontal in clockwise, the angle that summed with the 50° of the depression can be called α. Then:

 α+50=90

 α=90-50=40°

The trigonometric function than relates te two catheti with the angle α is:

tan(α)=opposite/adjacent

tan40=40/x

x=40/tan40=40/0.8390=47.7m

she will travel a distance in the range of 3 - 11 miles