Answer:
The ratios are;
[tex]\dfrac{BC}{AB} = \dfrac{3}{5}[/tex]
[tex]\dfrac{AC}{AB} = \dfrac{4}{5}[/tex]
[tex]\dfrac{BC}{AC} = \dfrac{3}{4}[/tex]
[tex]\dfrac{DE}{AD} = \dfrac{3}{5}[/tex]
[tex]\dfrac{AE}{AD} = \dfrac{4}{5}[/tex]
[tex]\dfrac{DE}{AE} =\dfrac{3}{4}[/tex]
Step-by-step explanation:
Given that the lengths of the sides are;
[tex]\overline {AB}[/tex] = 20
[tex]\overline {BC}[/tex] = 12
[tex]\overline {AC}[/tex] = 16
[tex]\overline {AD}[/tex] = 10
[tex]\overline {DE}[/tex] = 6
[tex]\overline {AE}[/tex] = 8
The ratios are;
[tex]\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{BC}{AB} = \dfrac{12}{20} = \dfrac{3}{5}[/tex]
[tex]\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AC}{AB} = \dfrac{16}{20} = \dfrac{4}{5}[/tex]
[tex]\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{BC}{AC} = \dfrac{12}{16} = \dfrac{3}{4}[/tex]
[tex]\dfrac{Length \ opposite \ \angle A}{Hypothenus} = \dfrac{DE}{AD} = \dfrac{6}{10} = \dfrac{3}{5}[/tex]
[tex]\dfrac{Length \ adjacent\ \angle A}{Hypothenus} = \dfrac{AE}{AD} = \dfrac{8}{10} = \dfrac{4}{5}[/tex]
[tex]\dfrac{Length \ opposite \ \angle A}{Length \ adjacent \ \angle A} = \dfrac{DE}{AE} = \dfrac{6}{8} = \dfrac{3}{4}[/tex]
