In triangle mno, mn=20, no=15, and mo=18. what is the approximate difference between the largest and smallest angle measures?

a) 2 degrees
b) 5 degrees
c) 14 degrees
d) 28 degrees

d) 28 degrees

Step-by-step explanation:

Be,

a = MN = 20

b = NO = 15

c = MO = 18

A = angle opposite side "a"

B = angle opposite side "b"

C = angle opposite side "c"

By the law of cosines, we know that,

Isolating "A" from the first equation we can clamp the angle opposite to the side "a", as follows

Replace the values and calculate the value of angle "A", like this

A = 73.98 ~ 74 degrees

Now calculate the value of angle B in a similar way,

Replace the values and calculate the value of angle "B", like this

B = 46.13 ~ 46 degrees

The sum of the angles of a triangle is 180 degrees, that is,

A + B + C = 180 degrees

Isolating C,

C = 180 - A - B

C = 180 - 74 - 46

C = 60

Being A = 74, B = 46, C = 60, then the approximate difference between the major and minor angle measures is,

Difference = A - C

Difference = 74 - 46

Difference = 28 degrees

Hope this helps!