Question 1:
(a) Using sine rule
ground/Sin 49 = plank/Sin 90
But sine 90 = 1, ground = 3 ft
Then,
3/Sin 49 = plank
Length of the plank = 3/Sin 49 ≈ 4.0 ft (rounded to nearest tenth)
(b) Height where the plank touches the wall
wall = Sqrt (plank^2 - ground^2) = Sqrt (4.0^2 - 3.0^2) ≈ 2.6 ft (Rounded to nearest tenth)
Question 2:
(a) Angle x
ground = 24 ft
support wire = 30 ft
Applying sine rule
support wire/Sin 90 = ground/Sin (90-x) ----- but Sin 90 = 1
Then,
Support wire = ground/Sin (90-x)
Sin (90-x) = ground/support wire = 24/30 = 0.8
90-x = Sin^-1(0.8) = 53.13 => x = 90-53.13 = 36.9°
(b) Height where the wire touches the tree (tree)
tree = Sqrt (support wire^2 - ground^2) = Sqrt (30^2 - 24^2) = 18 ft
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X represents elga’s age
x+14+x=98
combine like terms
2x+14=98
subtract 14 from both sides
2x=84
divide both sides by 2 to isolate the variable (x)
x=42
elga is 42 years old.
if alvin is 14 years older than elga, and elga is 42, then alvin is 56 years old. 42+56=98
This is the answer ig 2.449 kilograms