[tex]\huge \red \dag \underline {\rm {{{\color{orange}{Given ...}}}}} \red \dag[/tex]
- Diagonal of TV screen = 42 inches
- Base of TV screen = 38 inches
[tex]\huge \red \dag \underline {\rm {{{\color{orange}{To \: Find ...}}}}} \red \dag[/tex]
[tex]\huge \red \dag \underline {\rm {{{\color{orange}{Solution ...}}}}} \red \dag[/tex]
Answer according to the figure in attachment
In this situation we use Pythagoras theorem.
- Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
According to Pythagoras theorem
[tex]\Large❏ \: \Large\begin{gathered} {\underline{\boxed{ \tt {\blue{BD² = BC² + DC²}}}}}\end{gathered}[/tex]
- BD = 42 inches
- BC = 38 inches
- DC = ?
We need to find the DC.
Substituting the values in Pythagoras theorem
[tex]\large\purple\implies \tt \large \:BD² = BC² + DC²[/tex]
[tex]\large\purple\implies \tt \large \: {42}^{2} \: = \: {38}^{2} \: + \: DC²[/tex]
[tex]\large\purple\implies \tt \large \:1764 \: = \: 1444 \: + \: DC²[/tex]
[tex]\large\purple\implies \tt \large \:1764 \: - \: 1444 \: = \: DC²[/tex]
[tex]\large\purple\implies \tt \large \:320 \: = \: DC²[/tex]
[tex]\large\purple\implies \tt \large \: \sqrt{320} \: = \: DC[/tex]
[tex]\large\purple\implies \tt \large \:17.88 \: = \: DC[/tex]
Hence , the height of TV is 17.88 inches
