An observer (o) spots a plane (p) taking off from a local airport and flying at a 33° 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 7,000 ft., how far is the bird (b) from the plane (p)? round to the nearest whole number. two parallel lines b p and o t with a transversal running through p and o. dotted red line from p to t and from b to o. angle p o t is 33 degrees. the length of p t is 7000. the length of b p is x. 3815 feet 5873 feet 8343 feet 10,779 feet

Answer. Fourth option: 10,779 feet

Solution:

tan Angle POT = (Opposite leg) / (Adjacent leg)

tan 33° = PT / BP

PT=7,000 feet

tan 33° = 7,000 feet / x

Solving for x:

tan 33° x = 7,000 feet

Dividing both sides of the equation by tan 33°:

tan 33° x / tan 33° = 7,000 feet / tan 33°

x = 7,000 feet / tan 33°

x= 7,000 feet / 0.649407593

x = 10,779.05475 feet

x = 10,779 feet

sec ф = 5/3 (quadrant 4)

let x = base

y = perp

z = hypotenuse

sec ф = hypotenuse/base = 5/3

⇒ z = 5 and x = 3

finding y:

z² = x² + y²

5² = 3² + y²

y² = 25-9

y² = 16

y = 4

now finding all other geometric functions of theta:

sin ф = y/z = 4/5

sin ф = -4/5 (sin is negative in the 4th quadrant)

cos ф = x/z = 3/5

cos ф = 3/5 (cos is positive in 4th quadrant)

tan ф = y/x = 4/3

tan ф = -4/3 (tan is negative in 4th quadrant)

cosec ф = z/y = 5/4

cosec ф = -5/4 (cosec is negative in the 4th quadrant)

cot ф = x/y = 3/4

tan ф = -3/4 (tan is negative in 4th quadrant)

555.99.

step-by-step explanation:

hope this