A bird sitting on top of a stop sign notices a piece of food on the ground, 11 ft from the base of the stop sign. If the bird has to lool down at a 39 ° angle of depression in order to see the piece of food, what is the approximate distance from the bird to the food? (Assume the stop sign is at a right angle to the ground.)

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 and h the hypotenuse, then  

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

The food is approximately 14 feet from the bird

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

step by step resolutions

1) n+n+1+n+2=51

3n+3=51

3n=48

n=16

the three numbers are 16, 17 and 18.

2) x+15=4x

3x=15

x=5

radha is now 5 years old

3) the two digits are x and y.

y=3x

(10x+y)+(10y+x)=88

y=3x

11x+11y=88

y=3x

x+y=8

x+3x=8

x=2

the original number can be either 28 or 82.

4) n+(n+2)+(n+4)=48

3n+6=48

3n=42

n=14

the numbers are 14, 16 and 18.

5) y=x+3

10y+x+10x+y=143

y=x+3

11x+11y=143

y=x+3

x+y=13

x+x+3=13

2x=10

x=5

the original number can be 57 or 75.

hope this !