From the law of sines, we have

where
is the leg we're interested in,
is the hypothenuse,
is the angle opposite to
, and
is the angle between
and
.
So, in the first case, we can use

And in the second excercise, we use

Irrational
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11/12 as a fraction is 11/12; as a decimal it is ~ 0.9167
The probability that a high school student in in the marching band is 0.47
so, 
The probability that a student plays a varsity sport is 0.32
so, 
the probability that a student is in the marching band and plays a varsity sport is 0.24
so, we get
P(M∩V)=0.24
a student plays a varsity sport if we know she is in the marching band
so,
P(V|M)=(P(V∩M))/(P(M))
now, we can plug values
and we get


So,
the probability that a student plays a varsity sport if we know she is in the marching band is 0.51063......Answer
Using distance between two points to find the lengths of the edges of the triangle, the correct option is:
b. Isosceles
The distance between two points,
and
, is given by:

Vertex D is translated 4 units to the right is (9,8).
The lengths of the edges are:



<u>Two edges of the same length</u>, hence, it is an isosceles triangle, given by option b.
You can learn more about distance between two points at brainly.com/question/18345417