Geometry ? ?

1) a bird (b) is spotted flying 5,000 feet from a tree (t). an observer (o) spots the bird (b) at a distance of 13,000 feet. what is the angle of depression from the bird (b) to the observer (o)?
22.70°
44.62°
67.38°
68.96°

2) an observer (o) spots a plane (p) taking off from a local airport and flying at a 29° angle horizontal to her line of sight and located directly above a tower (t). the observer also notices a bird (b) circling directly above her. if the distance from the plane (p) to the tower (t) is 6,000 ft., how far is the bird (b) from the plane (p)? round to the nearest whole number.
6857 feet
10,824 feet
12,371 feet
22,063 feet

3) an observer (o) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. if the distance from the observer (o) to the bird (b) is 15,000 ft., how far is the bird (b) from its nest (n)? round to the nearest whole number.
8604 feet
12,287 feet
18,366 feet
21,422 feet

(1) C. 67.38°

(2) B. 10,824 feet

(3) A. 8604 feet.

Step-by-step explanation:

(1) We can see from our provided graph that bird, observer and tree form a right triangle. The side with length 5000 feet is adjacent and side with length 13,000 feet is hypotenuse of our given right triangle.

Since cosine relates the adjacent side and hypotenuse of a right triangle, so we can set an equation as:

Therefore,  the angle of depression from the bird (B) to the observer (O) is 67.38 degrees and option C is the correct choice.

(2) We can see from our provided graph that bird, plane and observer form a right triangle.  

The distance between point O and B will be also 6000 feet as lines OB and PT are parallel lines. The measure of angle BPO will be 29 degrees.

Since tangent relates the adjacent side and opposite sides of a right triangle, so we can set an equation as:

Therefore, the bird (B) is 10824 feet from the plane (P) and option B is the correct choice.

(3). We can see from our given diagram that the nest, bird and observer forms a right triangle. The side with length 15,000 ft is hypotenuse and side x is adjacent side for our given angle.

Since cosine relates the adjacent side and hypotenuse of a right triangle, so we can set an equation as:

Let us multiply both sides of our equation by 15,000.

Therefore, the bird is 8604 feet far from the nest and option A is the correct choice.

441

Step-by-step explanation: