#11 and #13 geometry help please help need work shown as well !!

In diagram (11) X = 30 degrees and Y = 60 degrees

In diagram (13) X = 20.55 degrees and Y = 69.45 degrees

Step-by-step explanation: What we have are two right angled triangles with two sides given in each case, therefore we can calculate the two unknown angles (since the third angle equals 90 degrees).

For the second triangle (number 13) we shall use Y as the reference angle. That means we have an opposite (the side facing the reference angle) which is 24 and we have an adjacent (the side that lies between the right angle and the reference angle) which is 9. Hence,

Tan Y = opposite/adjacent

Tan Y = 24/9

Tan Y = 2.6667

Checking with your calculator or table of values, 2.6667 = 69.45

Having two angles, which are 90 and 69.45, the third angle X can be computed as

X = 180 - (90 + 69.45)

Sum of angles in a triangle equals 180

X = 180 - 159.45

X = 20.55 and Y = 69.45

For the first triangle (number 11) we shall use X as the reference angle. We have two sides, the opposite (the side facing the reference angle) which is 3, and the hypotenuse (side facing the right angle) which is 6. Hence,

Sin X = opposite/hypotenuse

Sin X = 3/6

Sin X = 0.5000

Checking with your calculator or table of values,

X = 30 degrees.

Also, now that we have two angles we can easily compute the third angle as follows

Y = 180 - (90 + 30)

Sum of angles in a triangle equals 180

Y = 180 - 120

Y = 60

X = 30 and Y = 60

the thermometer is precise but not accurate

step-by-step explanation:

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.