A 10 foot long ladder is leaning against a vertical wall with the top of the ladder 8ft from the ground. What is the slope of the ladder? How far is the foot of the ladder from the wall? Can a 6 foot tall man walk under the ladder 1 foot from the wall? Justify your answer.
looks like plain ol' Pythagoras
base^2 + 8^2 = 10^2
bse^2 = 100-64 = 36
base = √36 = 6
slope = rise/run = height/base = 8/6 = 4/3
Make a sketch of the situation
Place the 6-ft man on the base 3 ft from the base.
Is he below the ladder or did his head hit the ladder?
Prove your conclusion with calculations.
a soccer game is being televised by a certain tv station. a camera is situated 10 meters away from the longer side of the soccer field and 7 meters from the middle part.
answer
To find the slope of the ladder, we can use the formula for slope, which is rise over run. In this case, the rise is the vertical distance from the foot of the ladder to the top of the ladder, which is 8ft. The run is the horizontal distance from the wall to the foot of the ladder. Let's call this distance 'd,' which is what we need to find.
By using the Pythagorean theorem, we can relate the rise, run, and the length of the ladder. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, the rise is one of the sides, and the run is the other side.
So, we have:
(Length of ladder)^2 = (Rise)^2 + (Run)^2
Since the length of the ladder is 10ft and the rise is 8ft, we can substitute these values into the equation:
10^2 = 8^2 + d^2
Simplifying this equation, we have:
100 = 64 + d^2
Subtracting 64 from both sides, we get:
36 = d^2
Taking the square root of both sides, we find:
d = 6ft
Therefore, the foot of the ladder is 6ft from the wall.
Now, to determine whether a 6ft tall man can walk under the ladder 1ft from the wall, we need to check if the height of the man plus the distance from the wall to the foot of the ladder is less than the length of the ladder.
The height of the man is 6ft, and we found that the distance from the wall to the foot of the ladder is 6ft. So, the total height is 6ft + 6ft = 12ft.
Since the total height is greater than the length of the ladder, which is 10ft, a 6ft tall man cannot walk under the ladder 1ft from the wall.
Therefore, the answer is no, a 6ft tall man cannot walk under the ladder 1ft from the wall.