Answer:
The food is approximately 14 feet from the bird
Step-by-step explanation:
Right Triangle
They are known by the fact that they have a 90° internal angle. The basic trigonometric ratios stand on right triangles. Being x the adjacent side (or leg) of an angle [tex]\theta[/tex] and h the hypotenuse, then
[tex]\displaystyle cos\theta=\frac{x}{h}[/tex]
Imagine the right triangle ABC, where the bird is at A, the right angle is at B (the base of the stop sign) and the food is at C. We know the distance from the stop sign to the food is x=11 ft, and the angle of depression from A is 39°. This angle is exactly the same as the one formed by x and the hypotenuse h, the distance from the bird to the food. Thus, solving for h
[tex]\displaystyle h=\frac{x}{cos\theta}[/tex]
[tex]\displaystyle h=\frac{11}{cos39^o}[/tex]
[tex]\boxed{h=14.15\ ft}[/tex]
The food is approximately 14 feet from the bird
