Question

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.

Answer 1

Answer:

The vertical distance from the ground to the bird's eyes is 47.67 m

Step-by-step explanation:

* Lets explain the situation of the problem

- There is a bird on the top of  a tree

- The bird looks down on a field mouse at an angle of depression of 50°

- The field mouse is 40 meters from the base of the tree

* Consider that the vertical distance from the ground to the bird's eyes,

 the distance from the field mouse to the base of the tree distance

 from the bird eyes to the field mouse formed a right triangle

- The hypotenuse is the distance from the bird eyes to the field mouse

- The horizontal side is the distance from the field mouse to the base

 of the tree

- The angle between the hypotenuse and the horizontal side is the

 angle of depression which = 50°

- The opposite side to the angle of measure 50° is the vertical distance

 from the ground to the bird's eyes

* Lets use trigonometry functions to find the vertical distance

∵ The length of the adjacent side to the angle of measure 50° is 40 m

∵ The length of the opposite side to the angle of measure 50° is h m

∵ tan Ф = opposite side to Ф ÷ adjacent side to Ф

∵ Ф = 50°

∴ tan 50° = h/40 ⇒ by using cross multiplication

∴ 40 tan 50° = h

∴ h = 47.67 m

* The vertical distance from the ground to the bird's eyes is 47.67 m