Question

In triangle ABC AC=2√10 if tan B =2 and tanC=3 find the length of the sides BC and AB

Answer 1

Answer

Given:-

AC length=2√10

tanb=2

tanc=3

ATQ,

tanc=>p/b=AB/BC=3

AB/BC=3

AB=3BC

By pythogorous theorm:-

AB²+BC²=AC²

=>(3BC)²+BC²=AC²

=>9BC²+BC²=AC²

=>10BC²=>AC²

=>BC²/AC²=1/10

=>AC²/BC²=10

=>AC/BC=√10

=>2√10/BC=√10 {putting the value of AC}

=>BC=2

So,AB=6 {put the value

Answer 2

AB = 6 units

BC = 2 units

................