Answer :
Answer:
The pigeon is 45.48 feet from the seed.
Step-by-step explanation:
Given:
Height of the barn = 28 ft
The angle of depression of bird seed from the pigeon is 38°
To find the distance of the pigeon from the bird seed.
Solution:
We can draw the situation with a right triangle.
The angle of depression is taken from top with the horizontal.
We are given the length of one leg of the triangle and a vertex angle. We need to find the hypotenuse of the triangle.
Let the hypotenuse of the triangle be = [tex]x[/tex]
Applying trigonometric ratio :
[tex]\sin 38\°=\frac{28}{x}[/tex]
Multiplying both sides by [tex]x[/tex]
[tex]x\sin 38\°=\frac{28}{x}\cdot x[/tex]
[tex]x\sin 38\°=28[/tex]
dividing both sides by [tex]\sin38\°[/tex]
[tex]\frac{x\sin 38\°}{\sin 38\°}=\frac{28}{\sin 38\°}\\[/tex]
∴ [tex]x=45.48[/tex]
Thus, the pigeon is 45.48 feet from the seed.
