Answer:
The altitude of triangle is 8 in.
Step-by-step explanation:
Solution :
Here, we have given that the two sides of triangle are 17 in and 15 in.
Finding the third side of triangle by pythagoras theorem formula :
[tex]{\longrightarrow{\pmb{\sf{{(Base)}^{2} + {(Altitude)}^{2} = {(Hypotenuse)}^{2}}}}}[/tex]
- [tex]\pink\star[/tex] Base = 15 in
- [tex]\pink\star[/tex] Hypotenuse = 17 in
- [tex]\pink\star[/tex] Altitude = ?
Substituting all the given values in the formula to find the third side of triangle :
[tex]\begin{gathered}\qquad{\longrightarrow{\sf{{(Base)}^{2} + {(Altitude)}^{2} = {(Hypotenuse)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(15)}^{2} + {(Altitude)}^{2} = {(17)}^{2}}}}\\\\\quad{\longrightarrow{\sf{{(15 \times 15)} + {(Altitude)}^{2} = {(17 \times 17)}}}}\\\\\quad{\longrightarrow{\sf{{(225)} + {(Altitude)}^{2} = {(289)}}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = {(289)} - (225)}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = 289 - 225}}}\\\\\quad{\longrightarrow{\sf{{(Altitude)}^{2} = 64}}}\\\\\quad{\longrightarrow{\sf{Altitude = \sqrt{64}}}}\\\\\quad{\longrightarrow{\sf{Altitude = 8 \: in}}}\\\\\quad{\star{\underline{\boxed{\sf{\red{Altitude = 8 \: in}}}}}}\end{gathered}[/tex]
Hence, the altitude of triangle is 8 in.
[tex]\rule{300}{2.5}[/tex]
