Question

Find the missing side. Step by step please. Thanks

Answer 1

`x= 33.6`

Explanation:

Working on left triangle ABC:

Applying Pythagorean theorem:

`AC^2=AB^2+BC^2\\`

Plunging in values

`AC=29 \ and \  AB=12`

`29^2=12^2+BC^2`

`841=144+BC^2`

Subtracting both sides by 144.

`841-144=144+BC^2-144`

`841=BC^2`

Taking square root both sides.

`√(697)=√(BC^2)`

`BC=26.4`

Working on left triangle ABD:

Applying Pythagorean theorem:

`AD^2=AB^2+BD^2\\`

Plunging in values

`AD=14 \ and \AB=12`

`14^2=12^2+BD^2`

`196=144+BD^2`

Subtracting both sides by 144.

`196-144=144+BD^2-144`

`52=BD^2`

Taking square root both sides.

`√(52)=√(BD^2)`

`BD=7.2`

`x=BD+BC= 7.2+26.4 =33.6`