In `Delta ABC , `right -angled at `B,AB=5cm and BC=12cm .` find the values of `sin A , sec A, sin C and secC.`

Explanation

In `Delta ABC ,angle B=90^(@),AB=5cm and BC=12cm`
By pythagoras ' theorem , we have
`AC^(2)=(AB^(2)+BC^(2))={(5)^(2)+(12)^(2)}cm^(2)`
`=(25+144)cm^(2)=169cm^(2)cm^(2).`
`therefore AC=sqrt(169cm^(2))=13cm`
For T-ratios of `angle A, ` We have
Base `=AB=5cm,`
perpendicular `=BC=12cm`
and hypotenuse `=AC=13cm.`
`therefore sin A=(BC)/(AC)=(12)/(13)and secA=(AC)/(AB)=(13)/(5).`
for T-ratios of `angle C,` we have
Base `=BC=12cm,`
perpendicular `=AB=5cm`
and hypotenuse `=AC=13cm.`
`therefore sin C=(AB)/(AC)=(5)/(13) and secC=(AC)/(BC)=(13)/(12).`