Answer:
Using the Similar Right Triangle theorem:
[tex]\mathsf{\dfrac{segment \ 1}{altitude}=\dfrac{altitude}{segment \ 2}}[/tex]
Given:
- segment 1 = 6
- segment 2 = 8
- altitude = [tex]x[/tex]
[tex]\implies \dfrac{6}{x}=\dfrac{x}{8}[/tex]
[tex]\implies 48=x^2[/tex]
[tex]\implies x=\sqrt{48}[/tex]
[tex]\implies x=\sqrt{16 \cdot 3}[/tex]
[tex]\implies x=\sqrt{16} \sqrt{3}[/tex]
[tex]\implies x=4\sqrt{3}[/tex]
[tex]\implies x=6.9 \textsf{ (nearest tenth)}[/tex]
