Question

`In `DeltaABC` , ltB=90^(@),tan A=( 3)/(4)`and length of BC =180 m, ten find the length of hypotenuse of `DeltaABC`.

Answer 1

We know that , tan `A=("perpendicular")/("base")=(BC)/(AB)=(3)/(4)`
So , let BC=3k and AB=4k
Form Pythagoras theorem,
` AC^(2)=AB^(2)+BC^(2)=(4k)^(2)+(3k)^(2)=25^(2)`
`:. AC=5k`
Now , since BC =180 cm (given)

`rArr 3k=180rArrk=60`
`:. AC=5k=5xx60=300`m
So , length of hypotenuse is 300m