Answer:
x=3.89
Step-by-step explanation:
I'll go in depth for you.
Before we figure out what we do, let understand what we know about this triangle.
- We know that both triangles have a angle that measure 27°.
- We also know EH=5
- FG=9
- ZG=7
- We need to know how to find EZ
Notice how line EG and HF intersect at Angle Z. We know that if two lines intersect at an angle, it form angles called vertical angles. This means that the two angles that are vertical to each other are congruent.
This means that angle Z in both triangles both measure the same.
Now since both triangles have 2 congruent corresponding angles, we can say that the Triangles are Similar due to the Angle-Angle Postulate.
"If two corresponding angles of two triangles are congruent, then the two triangles are similar."
What is mean when Triangles are similar?
It means that the similar triangles corresponding angles are equal and their sides are in proportion.
The corresponding sides are
EH and GF
EZ and ZG
HZ and HF.
Our proportion formula for similar triangles is
Any two sides of the first triangle divided by each other must equal the two corresponding sides of the second triangles divided by each other respectively.
We know FG and ZG so let set up our first fraction
[tex] \frac{fg}{zg} [/tex]
The corresponding sides of both are
- EH and EZ respectively so our proportion looks like
- [tex] \frac{fg}{zg} = \frac{eh}{ez} [/tex]
- Plug in the values for each. Let x represent the value of EZ
- [tex] \frac{9}{7} = \frac{5}{x} [/tex]
- Cross Multiply
- [tex]9x = 35[/tex]
- [tex]x = 3 \frac{8}{9} = 3.89[/tex]
- So x=3.89
