In ΔFGH, the measure of ∠H=90°, the measure of ∠G=64°, and HF = 72 feet. Find the length of FG to the nearest tenth of a foot.

9514 1404 393

  80.1 feet

Step-by-step explanation:

Side FH is opposite the given angle G, and side FG is the hypotenuse of the right triangle. The appropriate trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(64°) = (72 ft)/FG . . . . . substitute given values

  FG = (72 ft)/sin(64°)

  FG ≈ 80.1 ft

answer:

3 bags of apples and 2 bags of oranges.

step-by-step explanation:

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: