Question 1200752
you have:
sin(B) = 1/2
a = 20
a is opposite angle C
b is oppositge angle B
c is the hypotenuse which is opposite angle C which is the right angle of the right triangle.
if sin(B) = 1/2, then b = 1 and c = 2^2.
by pythagorus, a^2 + b^2 = c^2 gets you a^2 + 1^2 = 2^2
solve for a to get:
a = sqrt(2^2-1^2) = sqrt(4-1) = sqrt(3).
but a = 20, therefore there must a common factor in your right triangle that makes it similar to the larger triangle.
let that common factgor be x.
you get a = 20 in the larger triangle, while a = sqrt(3) in the smaller triangle.
the common factor tells you that 20 = sqrt(3) * x.
solve for x to get x = 20/sqrt(3)
since b in the smaller triangle is 1, then b in the larger triangle is 20/sqrt(3).
since c in the smaller triangle is 2, then c in the larger triangle is 2 * 20/sqrt(3) = 40/sqrt(3).
you get:
a = 20
b = 20/sqrt(3)
c = 40/sqrt(3)
by pythagorus, a^2 + b^2 = c^2 which gets you:
20^2 + (20/sqrt(3))^2 = (40/sqrt(3))^2
evaluate both sides of this equation to get:
533+1/3 = 533+1/3 which is simplified to 1600/3 = 1600/3, confirming the values of a, b, and c are correct.
not sure what you are looking for, but i get:
a = 20
b = 20/sqrt(3)
c = 40/sqrt(3)
since sine(B) = 1/2, then B must be equal to 30 degrees and A must be equal to 60 degrees, while C is 90 degrees.
bsically, you are dealing with similar triangles where the common factor is 20/sqrt(3), which says that the corresponding sides in the larger triangle are equal to the corresponding sides in the smaller triangle multiplied by a factor of 20/sqrt(3)