SOLUTION: iven right △ABC m∠N = o= 5.7 m∠M = n= 5 m∠O = 90° m=

Question 1189695: iven right △ABC
m∠N =

o= 5.7
m∠M =

n= 5
m∠O = 90° m=

Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
iven right △ABC
m∠N =

o= 5.7
m∠M =

n= 5
m∠O = 90° m=
~~~~~~~~~~~~~~~~~~

        G I B B E R I S H.

I regret about not destroying it immediately.

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I'm not sure why you mentioned triangle ABC, but I'll ignore that portion.

Drawing:

The diagram isn't to scale

Use the pythagorean theorem to find the missing side m
m^2 + n^2 = o^2
m^2 + 5^2 = (5.7)^2
m^2 + 25 = 32.49
m^2 = 32.49 - 25
m^2 = 7.49
m = sqrt(7.49)
m = 2.736786
That value is approximate

Now use the tangent ratio to help find angle M
tan(angle) = opposite/adjacent
tan(M) = m/n
tan(M) = 2.736786/5
M = arctan(2.736786/5)
M = 28.6944097
That value is approximate

Do the same idea for angle N
tan(angle) = opposite/adjacent
tan(N) = n/m
tan(N) = 5/2.736786
N = arctan(5/2.736786)
N = 61.3055903
That value is approximate

Or notice that
M+N = 90
N = 90-M
N = 90-28.6944097
N = 61.3055903

=============================================
Summary:

Side lengths:
m = 2.736786 (approximate)
n = 5
o = 5.7

Angles
M = 28.6944097 degrees (approximate)
N = 61.3055903 degrees (approximate)
O = 90 degrees

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