The slant edge of a cone is 17 cm long and its base diameter is 16cm . what is its vertical angle?
Did you make your sketch?
Then if the base angle is Ø
cosØ = 8/17 = .....
using my calculator Ø = appr 61.9°
take it from there, don't know how you defined "vertical angle"
To find the vertical angle of a cone, we can use the slant height and the radius of the base.
1. First, let's find the radius of the base. The diameter is given as 16 cm, so the radius is half of that:
Radius = Diameter / 2 = 16 cm / 2 = 8 cm
2. Now that we have the radius, we can use it along with the slant height to find the vertical angle. In a cone, the slant height (s) is related to the radius (r) and the height (h) by the Pythagorean theorem:
s^2 = r^2 + h^2
However, since we only want to find the vertical angle, we can ignore the height (as it is not given) and focus on the slant height and radius relationship.
3. Rearranging the equation, we have:
h^2 = s^2 - r^2
4. Substituting the given values, we have:
h^2 = (17 cm)^2 - (8 cm)^2
= 289 cm^2 - 64 cm^2
= 225 cm^2
5. Taking the square root of both sides, we have:
h = √225 cm
= 15 cm
6. Now we have the height of the cone (h), which is perpendicular to the base. The vertical angle of the cone can be calculated using the tangent function:
tan(θ) = h / r
Substituting the values we found:
tan(θ) = 15 cm / 8 cm
7. Calculating the tangent value, we get:
tan(θ) = 1.875
8. To find the angle itself, we can use the inverse tangent function (arctan):
θ = arctan(tan(θ))
= arctan(1.875)
Using a calculator, we find:
θ ≈ 63.43 degrees
Therefore, the vertical angle of the cone is approximately 63.43 degrees.
To find the vertical angle of the cone, we need to use the given information: the slant edge length (17 cm) and the base diameter (16 cm).
First, let's find the radius of the base. Since the diameter is given as 16 cm, we can divide it by 2 to get the radius:
Radius = Diameter/2 = 16 cm / 2 = 8 cm
Now, we can consider the right triangle formed by the slant height, the radius, and the height of the cone. The slant height of the cone is the hypotenuse of this triangle, the radius is one of the sides, and the height is the other side.
Using the Pythagorean theorem, we can find the height:
height = √(slant height^2 - radius^2)
height = √(17 cm^2 - 8 cm^2)
height = √(289 cm^2 - 64 cm^2)
height = √(225 cm^2)
height = 15 cm
Now that we have the height, we can find the vertical angle by using the inverse tangent function (arctan) on the height divided by the radius:
vertical angle = arctan(height / radius)
vertical angle = arctan(15 cm / 8 cm)
Using a scientific calculator or trigonometric table, we can find the arctan of 1.875:
vertical angle ≈ 63.4 degrees
Therefore, the vertical angle of the cone is approximately 63.4 degrees.