Answer:
The length of leg a is 5 m.
Step-by-step explanation:
As per given question we have provided that :
- [tex]\pink\star[/tex] Leg a: ? m
- [tex]\pink\star[/tex] Leg b: 3 m
- [tex]\pink\star[/tex] Hypotenuse c: 6 m
Here's the required formula to find the missing side of triangle :
[tex]{\longrightarrow{\pmb{\sf{{(a)}^{2} + {(b)}^{2} = {(c)}^{2}}}}}[/tex]
- [tex]\purple\star[/tex] a = ?
- [tex]\purple\star[/tex] b = 3 m
- [tex]\purple\star[/tex] c = 6 m
Substituting all the given values in the formula to find the third side of triangle :
[tex]\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 \times 3) = (6 \times 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 = \sqrt{25}}}}\\\\\qquad{\implies{\sf{\underline{\underline{a = 5 \: m}}}}}\end{gathered}[/tex]
Hence, the value of a is 5 m.
[tex]\rule{300}{2.5}[/tex]
