the other leg is √105
Explanation:Given:
Hypotenuse = 13
one of the legs of the triangle = 8
To find:
the other leg of the triangle
The triangle is right-angled. So, to get the third side, we will apply Pythagoras theorem:
Hypotenuse² = opposite² + adjacent²
let opposite = leg 1 = 8
adjacent = leg 2
Hypotenuse² = = leg1² + leg2²
[tex]\begin{gathered} 13^2=\text{ 8}^2\text{ + leg}_2^2 \\ \\ 169\text{ = 64 + leg}_2^2 \\ \\ 169\text{ - 64 = leg}_2^2 \\ \\ 105\text{ = leg}_2^2 \end{gathered}[/tex][tex]\begin{gathered} square\text{ root both sides:} \\ \sqrt{105}\text{ = leg}_2 \\ Can^{\prime}t\text{ be reduced an further inradical form} \\ \\ leg_2\text{ = }\sqrt{105}\text{ } \end{gathered}[/tex]Hence, the other leg is √105
