Answers:
Height = 4 feet, 1 inch
Distance from Base of ladder to bottom of slide = 6 feet, 10 inches
These values are approximate (rounded to the nearest inch)
side notes:
4 feet, 1 inch = 49 inches
6 feet, 10 inches = 82 inches
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The right triangle has
one leg that is 3x. Call this 'a', so a = 3x
another leg that is 5x. Call this b. So b = 5x
the hypotenuse is 8, so c = 8
Pythagorean theorem
a^2 + b^2 = c^2
(3x)^2 + (5x)^2 = 8^2
9x^2 + 25x^2 = 64
34x^2 = 64
x^2 = 64/34
x^2 = 32/17
x = sqrt(32/17)
x = 1.37198868114008
Use this x value to find that...
height = 3*x = 3*1.37198868114008 = 4.11596604342024 feet approximately
Convert the decimal part to inches (multiply by 12)
0.11596604342024*12 = 1.39159252104289 which rounds to 1 inch
The height of the slide is 4 ft, 1 inch roughly (4 ft, 1 inch = 49 inches)
Do the same for the horizontal distance as well
5*x = 5*1.37198868114008 = 6.8599434057004
multiply the decimal part by 12
12*0.8599434057004 = 10.3193208684049 which rounds to 10
The horizontal distance is roughly 6 ft, 10 inches (6 ft, 10 inches = 82 inches)
