The diagonal of a tv is 30 inches long. assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact length and width of the tv? a: 15 inches by 15√3 inchesb: 60 inches by 60√3 inchesc: 15√2 inches by 15√2 inchesd: 60√2 inches by 60√2 inches

Your answer is A: 15 inches by 15√3 inches.

We can use trigonometry to solve this. If we draw out one of the triangles we can label the 30 inch side as the hypotenuse, and then the other sides as the opposite and adjacent. Then we just have to find the lengths of these.

To find the opposite, we use the trigonometric ratio sinθ = opposite ÷ hypotenuse, and thus the opposite is sin(60) × 30 = 15√3

Automatically now we know the answer is A because that is the only option with 15√3 as a side, but you could also solve using cosθ = adjacent ÷ hypotenuse and get the other side.

I hope this helps!

the third picture

step-by-step explanation:

"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: