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

You are given BC and AC, lets find AB by using the Pythagorean theorem:

AB = √(20^2 - 16^2)

AB = √(400-256)

AB = √144

AB = 12

Since the triangles are similar, sin F would be the same as sin C

SinC = Opposite side / hypotenuse

SinC = 12/20, reduces to 3/5

SinF = SinC = 3/5

Then if you need the angle of F:

F = arcsin(3/5) = 36.87 degrees.

Sin F = 3/5

Step-by-step explanation:

Since F= C because the triangles are similar

Sin F  = Sin C  since the triangles are similar

sin C = opposite / hypotenuse

         =AB/AC

We know AC =20, but we need to determine AB

Since this is a right triangle

AB^2 + BC^2 = AC^2

AB^2 +16^2 = 20^2

AB^2 + 256=400

Subtract 256 from each side

AB^2 +256-256 = 400-256

AB^2 =144

Take the square root of each side

sqrt(AB^2) =sqrt(144)

AB = 12

sin C = 12/20

Divide the top and bottom by 4

sin C = 3/5

Sin F = 3/5

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows:

45

step-by-step explanation: