Question

Help this poor soul with the homework (•‿•)

find the length of the missing side of the triange shown below. round to the nearest tenth,if nessesary
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Answer 1

The altitude of triangle is 8 in.

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 :

`{\longrightarrow{\pmb{\sf{{(Base)}^(2) + {(Altitude)}^(2) = {(Hypotenuse)}^(2)}}}}`

• 
  `\pink\star` Base = 15 in
• 
  `\pink\star` Hypotenuse = 17 in
• 
  `\pink\star` Altitude = ?

Substituting all the given values in the formula to find the third side of triangle :

`\begin{gathered}\qquad{\longrightarrow{\sf{{(Base)}^(2) + {(Altitude)}^(2) = {(Hypotenuse)}^(2)}}}\\\\\quad{\longrightarrow{\sf{{(15)}^(2) + {(Altitude)}^(2) = {(17)}^(2)}}}\\\\\quad{\longrightarrow{\sf{{(15 * 15)} + {(Altitude)}^(2) = {(17 * 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 = √(64)}}}\\\\\quad{\longrightarrow{\sf{Altitude = 8 \: in}}}\\\\\quad{\star{\underline{\boxed{\sf{\red{Altitude = 8 \: in}}}}}}\end{gathered}`

Hence, the altitude of triangle is 8 in.

`\rule{300}{2.5}`

Answer 2

8 inches

Explanation:

Use Pythagorean theorem,

Base² + altitude² = hypotenuse²

15²+ altitude² = 17²

225 + altitude² = 289

altitude² = 289 - 225 = 64

altitude = √64 = 8 in