Question

pls help1. convince yourself the triangles are similar2. write 3 similarity statements3. determine the scale factor for each pair of triangles4. determine the lengths of sides HG, GF, and HF.

Answer 1

Angle HEG is 37 because the sum of all angles f a triangle is 180 and 180-90-53=37

The same way we find the angle GEF

2) the triangles are similar because they have the same shape, however they are located differently

the angle measures are equal

has a scaling factor

3)to solve the scale we can divide two measures that are equivalent on this case

`(16)/(12)=(4)/(3)`

4)

we can solve HG and then calculate GF using the scale

HG

`\begin{gathered} \sin (37)=(HG)/(12) \\ \\ HG=12\sin (37) \\ \\ HG=7.22 \end{gathered}`

multiplying by the factor we find GF

`\begin{gathered} 7.22*(4)/(3)=HG \\ \\ HG=9.62 \end{gathered}`

HF is the sum of HG abd GF, then

`\begin{gathered} 7.22+9.62=HF \\ HF=16.84 \end{gathered}`