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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.

Pls Help1 Convince Yourself The Triangles Are Similar2 Write 3 Similarity Statements3 Determine The Scale Factor For Each Pair Of Triangles4 Determine The Lengt class=

Sagot :

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

[tex]\frac{16}{12}=\frac{4}{3}[/tex]

4)

we can solve HG and then calculate GF using the scale

HG

[tex]\begin{gathered} \sin (37)=\frac{HG}{12} \\ \\ HG=12\sin (37) \\ \\ HG=7.22 \end{gathered}[/tex]

multiplying by the factor we find GF

[tex]\begin{gathered} 7.22\times\frac{4}{3}=HG \\ \\ HG=9.62 \end{gathered}[/tex]

HF is the sum of HG abd GF, then

[tex]\begin{gathered} 7.22+9.62=HF \\ HF=16.84 \end{gathered}[/tex]

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