Answer:
x = 14.4
Step-by-step explanation:
x is sin(angle 24/30)×24
how do we get the angle at 24/30 ?
by using the extended Pythagoras for baselines opposite other than 90 degrees.
c² = a² + b² - 2ab×cos(angle opposite of c)
in our example the angle 24/30 is opposite of the side 18.
so,
18² = 24² + 30² - 2×24×30×cos(angle 24/30)
324 = 576 + 900 - 1440×cos(angle 24/30)
324 = 1476 - 1440×cos(angle 24/30)
1440×cos(angle 24/30) = 1152
cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5
angle 24/30 = 36.9 degrees
x = sin(36.9) × 24 = 14.4
Answer:
The length of the building's shadow = 550.66 ft
Explanations:
The height of the Empie State Building = 1250 feet
The friend's height = 75 inches
The length of the friend's shadow = 33 inches
Take -5x + y =13 and rearrange for y:
y=13+5x
Substitute into other equation for y:
-3x+3(13+5x)=3
Multiply out brackets:
-3x+39+15x=3
Simplify:
12x+39=3
Rearrange for x:
12x=-36
x=-3
Substitute back into y=13+5x:
y=13+5(-3)
y=13-15
y=-2
Answer:
12/17
Step-by-step explanation:
total number of marbles that are purple (11) plus the total number of marbles that are not small (15) minus the number of marbles that are both purple and not small (2)
11 + 15 - 2 = 24
over the total number of marbles (34)
24/34 simplifies to 12/17
