Question

4. leg a: ? m leg b: 3 m b hypotenuse c: 6 m​

Answer 1

The length of leg a is 5 m.

Step-by-step explanation:

As per given question we have provided that :

• 
  `\pink\star` Leg a: ? m
• 
  `\pink\star` Leg b: 3 m
• 
  `\pink\star` Hypotenuse c: 6 m

Here's the required formula to find the missing side of triangle :

`{\longrightarrow{\pmb{\sf{{(a)}^(2) + {(b)}^(2) = {(c)}^(2)}}}}`

• 
  `\purple\star` a = ?
• 
  `\purple\star` b = 3 m
• 
  `\purple\star` c = 6 m

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

`\begin{gathered} \qquad{\implies{\sf{{(a)}^(2) + {(b)}^(2) = {(c)}^(2)}}}\\\\\qquad{\implies{\sf{{(a)}^(2) + {(3)}^(2) = {(6)}^(2)}}}\\\\\qquad{\implies{\sf{{(a)}^(2) + (3 * 3) = (6 * 6)}}}\\\\\qquad{\implies{\sf{{(a)}^(2) + (9) = (36)}}}\\\\\qquad{\implies{\sf{{(a)}^(2) + 9 = 36}}}\\\\\qquad{\implies{\sf{{(a)}^(2) = 36 - 9}}} \\\\\qquad{\implies{\sf{{(a)}^(2) = 25}}}\\\\\qquad{\implies{\sf{a = √(25)}}}\\\\\qquad{\implies{\sf{\underline{\underline{a = 5 \: m}}}}}\end{gathered}`

Hence, the value of a is 5 m.

`\rule{300}{2.5}`

Answer 2

a = 5 m

Explanation:

use
`a^2+b^2+c^2` :

`a^2+3^2=6^2\\ a^2+9=36\\ a^2=36-9\\ a^2=25\\ a=√(25) \\ a=5`