# In ΔABC, m∠B = 90, find the measure of the parts of the triangle other than the ones which are given below:(1) m∠C = 45, AB = 5(2) m∠A = 30, AC = 10(3) AC = 6√2, BC = 3√6(4) AB = 4, BC = 4

(1) If C = 45 and B = 90

A = 45 (angle sum property of a triangle)

A = C

AB = BC (sides opposite to equal angles)

and since, AB = 5

BC = 5

and by Pythagoras theorem

AB2 + BC2 = AC2

52 + 52 = AC

AC = 5√2

(2) if A = 30 and B = 90

C = 60 (Angle sum property of triangle)

put the known values

also,

(3)

C = 30

A = 60 (by angle sum property)

also, by Pythagoras theorem

AB2 = AC2 – BC2

AB = 3√2

(4) Since B = 90

AB2 + BC2 = AC2

substituting AC = 4 and BC = 4

we get

AC = 4√2

Also since, AB = BC

A = C (angles opposite to equal sides of the same triangle)

B = 0

A = C = 45 (Angle sum property)

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