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
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.
Great. Thanks for the answer
thank you
To find the radius of the base of the cone, you can use trigonometry and the given information.
First, note that the vertical angle is the angle between the axis of the cone and one of its slant height. Since the axis is perpendicular to the base, this vertical angle is also the angle formed between the slant height and the radius of the base.
We can use the tangent function (tan) to find the ratio between the slant height and the radius. The formula is:
tan(angle) = slant height / radius
In this case, the angle is 54 degrees and the slant height is 6 cm. Let's use x to represent the radius of the base. Rearranging the formula, we have:
tan(54 degrees) = 6 cm / x
Next, we can solve for x by multiplying both sides of the equation by x:
tan(54 degrees) * x = 6 cm
To isolate x, divide both sides of the equation by tan(54 degrees):
x = 6 cm / tan(54 degrees)
Using a calculator, the approximate value of tan(54 degrees) is 1.3764. Therefore:
x = 6 cm / 1.3764
Calculating this gives us:
x ≈ 4.1292 cm
Hence, the radius of the base of the cone is approximately 4.1292 cm.