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In a right angled triangle ABC, AB=2.5 "...

In a right angled triangle ABC, `AB=2.5 "cm" cos B=0.5 /_ ACB= 90^(@)` Then length of side AC is?

A

`(5)/(4) sqrt(3)`

B

`(5)/(16) sqrt(3)`

C

`5 sqrt(3)`

D

`(5)/(2) sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`cos B = 0.5^(@)` `cos B = cos 60^(@)`
B = 60
`sin 60^(@) =(AC)/(AB)`
`rArr (sqrt(3))/(2)=(x)/(2.5)`
`(x)/(2.5)=(sqrt(3))/(2)`
`x = (sqrt(3)xx25^(@))/(20)`
`=(5 sqrt(3))/(4)`
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