Question

In triangle abc angle b = 90 and angle c = 60 angle A = 30 ,ac = 18 find bc and ab

Answer 1

ANSWER:

BC=9

AB=18/√2

Step-by-step explanation:

Given

b=90

c=60

a=30

ac=18

to find

bc

ab

solution

bc= ½ Hypotenuse ..... 30-60-90 angle theorem

bc=½ac

bc=½18

bc=9

ab= Hypotenuse /√2......30-60-90angle theorem

ab=ac/√2

AB=18/√2

Answer 2

Answer:

Thus BC=9 cm and AB=9√3

Purposely I did not use trigonometry

Step-by-step explanation:

In the fig at AC we take D such that

BD=BC

Thus ∠DBC=∠DCB=60

so ∠BDC=180-(60+60)=60

Thus ΔBCD is an equilateral

So BC=CD=BD

in ΔBCD =90-∠DBC=90-60=30

So∠DAB=∠ABD=60

So AD=BD=CD

so D is mid point Of ACTHus BC=1/2Ac=18/2=9

AB=√(AC²-BC²)

=√(18²-9²

=√(324-81)

=√243 =√(81*3

=9√3

Thus BC=9 cm and AB=9√3

Puposely I did not use trigonoimetry