Respuesta :
Answer:
Angle F = m∠C = 20°
Angle E = m∠B = 70°
AC = 11.3 cm
DF = 5.6 cm
DE = 2.0 cm
Explanation:
the triangle is right angle triangle
I \C
20
I \
I \12 cm
I \
AI_4.1cm__\B the triangle is right angle triangle
I \F
I \
I \6cm
I \
DI_______\E
AC will be calculated by using pythagorean theorem
AC ^2 = BC^2 - AB^2
AC^2 = 127.19
AC = 11.3 cm
To calculate DF, we will use similarity method
AC/BC = DF/EF
11.3/12 = DF/6
DF = 5.6 cm
We will use the same similarity method to calculate DE
AC/AB = DF/DE
11.3/4.1 = 5.6/DE
DE = 2.0 cm
m∠B = 90 - 20 = 70
Therefore m∠B = 70°
m∠E = 70°, same as m∠B = 70°
Angle F = m∠C = 20°
The corresponding angles and corresponding sides are shown below,
[tex]\angle A=\angle D=90\\\\\angle B=\angle E=70\\\\\angle C=\angle F=20[/tex] and [tex]DE=2.05cm, EF=6cm[/tex]
Similar triangles:
It is given that, ΔABC ∼ ΔDEF
When two triangles are similar, Then, corresponding angles are equal and corresponding sides are in equal proportion.
So that, [tex]\frac{AB}{DE}=\frac{BC}{EF} =\frac{AC}{DF}[/tex]
[tex]\angle A=\angle D\\\\\angle B=\angle E\\\\\angle C=\angle F[/tex]
Given that, m ∠A = 90°, m ∠C = 20°, BC ≈ 12 cm, AB ≈ 4.1 cm and
EF =6cm.
[tex]\angle A=\angle D=90\\\\\angle B=\angle E=70\\\\\angle C=\angle F=20[/tex]
Ratio of corresponding sides are,
[tex]\frac{AB}{DE}=\frac{BC}{EF} \\\\\frac{4.1}{DE}=\frac{12}{6}\\ \\ DE=2.05cm[/tex]
Hence, the corresponding angles and corresponding sides are shown below,
[tex]\angle A=\angle D=90\\\\\angle B=\angle E=70\\\\\angle C=\angle F=20[/tex] and [tex]DE=2.05cm, EF=6cm[/tex]
Learn more about the similar triangle here:
https://brainly.com/question/2644832
