In triangle abc, the measure of ∠b is 90°, bc=16, and ac=20. triangle def is similar to triangle abc, where vertices d, e, and f correspond to vertices a, b, and c, respectively, and each side of triangle def is

1/3

the length of the corresponding side of triangle abc. what is the value of sinf?

Step-by-step explanation:

From.the Pythagoras theorem,

DF² = DE² + EF²; therefore, DE²= DF²-EF².since each of the side of DEF is 1/3 of sides ABC , it implies that ,1/3 of 20 = 6.7 ( DF)and 1/3 of 16 = 5.3 (EF)

DE² = 6.7²-5.3²;

DE² = 44.89 - 28.09

DE² =16.8

Therefore taking the square root is both side to get the true value of DE

√DE² = √16.8; DE = 4.098.

there the value of sin of angle F

SinF°= 4.098/6.7; = 0.6116

Therefore F° = sin-¹0.6116; 37.7°.

SinF = 0.6116, while angle F = 37.7°

Note: the purpose of using the Pythagoras theorem is to help you find the third side of triangle DEF which is DE

b

step-by-step explanation:

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.