Question

Calculate AH and HC ​

Answer 1

AH=9

HC=40

Explanation:

In ΔABH

∡H=90°

AB=15

BH=12

AH=?

here we can use Pythagoras' theorem:

`a^2+b^2=c^2` where a is base b is perpendicular and c is hypotenuse.

substituting value

`12^2+AH^2=15^2`

`AH^2=15^2-12^2`

`AH^2=81`

`AH=√(81)=9`

Therefore: AH=9

In ΔACH

∡H=90°

AH=9

HC=?

∡C=30°

here also we can use Pythagoras' theorem:

`a^2+b^2=c^2` where a is base b is perpendicular and c is hypotenuse.

substituting value

`HC^2+9^2=41^2`

`HC^2=41^2-9^2\\HC^2=1600\\HC=√(1600)=40`

Therefore, HC=40