Please help me find the value of x the answer must be exact

Step-by-step explanation:

This is a 45°-45°-90° triangle. The two legs are the same length, and the hypotenuse is that length times the square root of two:

Therefore, the value of x is 11.

You can double-check using the sine ratio:

Insert the values:

Insert the equation into a calculator:

:Done

*It's important to know that, when working with trigonometry ratios, the hypotenuse is never considered the adjacent or opposite side, and the 90° angle is never used in the ratios.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.