Q. 35.0( 4 Votes )

In ΔABC, mB = 90, find the measure of the parts of the triangle other than the ones which are given below:

(1) mC = 45, AB = 5

(2) mA = 30, AC = 10

(3) AC = 6√2, BC = 3√6

(4) AB = 4, BC = 4

Answer :


(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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