Question

In the given figure, <B = 60°, AB = 8 cm and BC = 25 cm. Calculate:

( I ) AB
( II ) AC

Answer 1

Solution :

It is given that ,

In ∆ABE , <B = 60° , AB = 8 cm

<AEB = 90°

Now,

i ) In ∆ABE ,

cos 60° = BE/AB

=> 1/2 = BE/8

=> 8/2 = BE

=> 4 = BE

ii ) Sin 60° = AE/AB

=> √3/2 = AE/8

=> 8√3/2 = AE

=> 4√3 = AE

=>AE = 4√3 cm

iii )EC= BC - BE

=> EC = 25 - 4 = 21 cm

Now ,

In ∆AEC , <AEC = 90°

By Phythogarian theorem,

AC² = AE² + EC²

= ( 4√3 )² + 21²

= 48 + 441

= 489

AE = √489

≈ 22.11 cm

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Answer 2

thank you your help