Step One
Find z
All triangles have 180 degrees. No exceptions.
z + 47 + 90 = 180 combine like terms on the left.
z + 137 = 180 subtract 137 from both sides
z = 180 - 137
z = 43 degrees.
Step Two
Use the sine function to find y
Sin(43) = opposite side / hypotenuse
opposite side = 35
sin(43) = 35 / hypotenuse
hypotenuse = 35 / sin(43)
y = 35/0.6820
y = 51.32
Solve using cos(x)
Note this problem could have been done in a shorter way.
Cos(47) = adjacent / hypotenuse.
hypotenuse = adjacent / cos(47)
y = 35 / cos(47)
y = 35 / 0.6820
y = 51.32 Both answers agree. It is a good thing to know how to do this question both ways.
1. (-1,-1) (2,-2)
2. (-3,0) (2,0)
3. (-4,-3) (-1,2)
Answer:
1.66666666667
Step-by-step explanation:

has CDF

where

is the CDF of

. Since

are iid. with the standard uniform distribution, we have

and so

Differentiate the CDF with respect to

to obtain the PDF:

i.e.

has a Beta distribution

.