Question

If triangle abc is similar to triangle def, angle a=30°, angle c=50°, ab=5cm, ac=8cm and df=7.5cm then find de and angle f.

Answer 1

The angle F measure is 50 degrees and DE have length of 4.68 cm.

Step-by-step explanation:

We are given the following in the question:

Triangle ABC is similar to triangle DEF.

$\angle A=30^\circ \\\angle C=50^\circ\\AB=5~cm\\AC=8~cm\\DF=7.5~cm$

Since the triangle are similar, they share the following properties:

$\angle A =\angle D\\\angle B =\angle E\\\angle C =\angle F$

Thus,

$\angle F = 50^\circ$

Also, the ration of corresponding sides of similar triangle are equal. Thus, we can write,

$\displaystyle\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Puting, the values, we get,

$\displaystyle\frac{AB}{DE}=\frac{AC}{DF}\\\\\frac{5}{DE}=\frac{8}{7.5}\\\\DE = \frac{5\times 7.5}{8} = 4.68~cm$

The angle F measure is 50 degrees and DE have length of 4.68 cm.

#LearnMore

If triangle ABC is similar to triangle DEF , angle A=30, angle c=50,AB=5cm

AC=8cm,DF=19.2cm .Then which of the following is true

A) angle E=50,DF=12cm

B) angle D=30,EF=12cm

C) angle E=100,DE=12cm

D) angle D=100,EF=12cm​

https://brainly.in/question/12498452

Answer 2

If triangle abc is similar to triangle def, angle a=30°, angle c=50°, ab=5cm, ac=8cm and df=7.5cm then find de and angle f.