From an angle of depression of 61 degrees, John watches his friend approach his building while standing
on the rooftop. The rooftop is 17 m from the ground,
and John's eye level is at about 2m from the ground.
What is the distance between John's friend and the
building?
10.6
34.3
5.5
10.5

10.53

Step-by-step explanation:

Given :

Height of building = 17m

John's eye level = 2 m

Total height (including eye level) = 17+2 = 19m

Angle of depression, θ = 61°

Let distance between John's friend and building = d

Using trigonometry :

Tan θ = opposite / Adjacent

Tan 61° = 19 / d

1.8040477 = 19 / d

d = 19 / 1.8040477

d = 10.53

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.

answer: integers are just whole numbers: positive, negative, and zero.

i = {-∞, -2, -1, 0, 1, 2, 3, ∞}

let x = 1st integer

let y = 2nd integer

x = 3y + 17   {equation 1}

xy = -24         {equation 2}

substitute 3y+17 in place of x n equation 2

and solve for y.

(3y+17)y = -24

3y2 + 17y = -24

3y2 + 17y + 24 = 0

from quadratic equation:

y = [-17±√(172-4(3)(24))]/(2(3))

y = (-17 ±√1)/6

y = (-17+1)/6   or     y = (-17-1)/6

y = -16/6           or     y = -18/6

y = -2 2/3         or   y = -3

since we are dealing with

y = -3

x = 3y+17 = -9+17 = 8

the integers are -3, 8

step-by-step explanation: