On a softball field, home plate is 43 feet from the pitcher's mound. A ball is hit at an angle of 27° east of the pitcher's mound. The ball travels 162 feet before it is caught by an outfielder. A triangle is drawn on a baseball field. A point is at home plate, another point is at the pitcher apostrophe s mound, and another point is at an outfielder. The distance from home plate to the pitcher is 43 feet. The distance from home plate to the outfielder is 162 feet. The angle between the 2 sides is 27 degrees. Law of cosines: How far must the outfielder throw the ball to return it to the pitcher? Round to the nearest foot. 112 feet 125 feet 145 feet 156 feet

c  =  125  f

Step-by-step explanation:

Let´s call points  A ( home plate )  B (pitcher´s place ) and C ( outfielder place)

these three points form a triangle in which according to cosine law, one side of a triangle c  can be calculated by the equation:

c²  =  a²  +  b²  - 2a*b*cos∡a,b

a and  b are the other sides of the triangle and ∡a,b is the angle between sides a and b

All distances are in feet then the distance between  outfielder and pitcher  (c) is in feet:

c² = (43)²  +  ( 162)²  - 2*(43)*(162)*cos 27°            cos 27°  = 0,891

c²  = 1849 +  26244 - 12413,4

c²  =  15679,6

c = √15679,6

c  =  125  f

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:

25% is the answer