Question

A cone is 6cm high and its vertical angle is 54degrees. Calculate the radius of its base.
MY ANSWER
tan54=x/6(let x be the radius)
6*tan54=x
6*1,3764=x
8,2584=x
8,2584/2=x
4,1292cm=x

Answer 1

NO
first of all you are using x incorrectly

(in the third last line x = 8,2584, and in the last line x = 41292, which is a contradiction)
furthermore, we place a comma after groups of 3 digits for easier reading, not groups of 4 digits.
furthermore #2, if the height is 6 cm, did it not appear totally irrational for the radius to be 41292 cm ??

now to the actual question ....

make a sketch, draw in the height
you will have a right-angled triangle with
height = 6, radius = r, angle at the top 27°
NOW, tan27 = r/6
r = 6tan27 = 3.057 cm or 3.1 cm to one decimal

to use 54°, would not even give you a right-angled triangle, so the rest of your solution is bogus.

Answer 2

Great. Thanks for the answer

Answer 3

thank you