Paul is locked out of his house. An 18-ft ladder is outside and an upstairs window is open. Paul read the safety warning on the ladder recommending it be placed six feet away from the wall. He placed the ladder according to the warning and it reached the base of the window. How high is the base of the window off the ground?

17.0 ft

Step-by-step explanation:

Let h be the height of the base of the window from the ground, L be the length of the ladder = 18 ft and d be the distance of the ladder from the wall = 6 ft. Now, these three lengths form a right-angled triangle with the length of the ladder, L as the hypotenuse side.

So, using Pythagoras' theorem,

L² = h² + d²

So, h = √(L² - d²)

Substituting the values of L = 18 ft and d = 6 ft, we have

h = √((18 ft)² - (6 ft)²)

= √(324 ft² - 36 ft²)

= √288 ft²

= 16.97 ft

≅ 17.0 ft

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: