Answer:
3/2 = 6/4
Step-by-step explanation:
Given that ∆BDE ~ ∆BAC by dilation of a scale factor of 2, it means therefore that:
BA/BD = BC/BE = AC/DE = 2
BD = 2
BA = 2*BD = 2*2 = 4
BE = 3
BC = 2*BE = 2*3 = 6
DE = 3.61
AC = 2*DE = 2*3.61 = 7.22
Also:
<D = <A,
<E = <C
=>Find tan <D, and tan <A using trigonometric function to determine which proportion gives us tan<D = tan<A
Tan<D = opposite/adjacent
Tan<D = BE/BD
Tan<D = 3/2
Tan<A = opposite/adjacent
Tan<A = BC/BA
Tan<A = 6/4 = 3/2
<em>Therefore, the proportion that proves that tan<D = tan<A is:</em>
<em>BE/BD = BC/BA = 3/2 = 6/4</em>
