the vertical angle of a cone is 70 degree and its slant height is 11cm. Calculate the height of the cone
draw a side view and you can see that
h/11 = cos(70/2)°
Well, well, well, looks like we need to do some math with cones! Alright, let's get to it.
First things first, we need to use that vertical angle of 70 degrees and the slant height of 11cm to figure out the radius of the cone's base.
To do that, we can use some trigonometry. The sine of the vertical angle is equal to the ratio of the height (h) to the slant height (l). So, we have:
sin(70°) = h / 11
To solve for h, we multiply both sides of the equation by 11:
h = 11 * sin(70°)
Now, let's grab our calculators for a moment... crunch, crunch, crunch... and we find:
h ≈ 9.81 cm
So, the height of the cone is approximately 9.81 cm. Hope that helps, and happy cone calculations!
To find the height of the cone, we can use the concept of trigonometry.
Given:
Vertical angle of the cone = 70 degrees
Slant height of the cone = 11 cm
First, let's label the different parts of the cone:
/|
/ |
/ |
h / | slant height (s)
/ |
/ |
/α_____|
\ r /
Where:
h = height of the cone
r = radius of the base of the cone (which is not given)
Now, we can find the height using trigonometry.
Since we know the slant height (s) and the angle (α), we can use the trigonometric sine function.
sin(α) = opposite/hypotenuse
In this case, the opposite side is the height of the cone (h), and the hypotenuse is the slant height (s).
sin(α) = h / s
Let's substitute the given values into the equation:
sin(70°) = h / 11 cm
Now, we can solve for h:
h = sin(70°) * 11 cm
Using a calculator:
h ≈ 10.26 cm
Therefore, the height of the cone is approximately 10.26 cm.
To calculate the height of the cone, we can use trigonometry.
The slant height (l) and the vertical angle (θ) can be used to find the height (h) using the trigonometric relationship:
sin(θ) = h / l
In this case, the vertical angle is given as 70 degrees and the slant height is given as 11 cm.
First, convert the angle from degrees to radians:
θ_rad = θ_deg * π / 180
= 70 * π / 180
≈ 1.2217 radians
Then, plug in the given values into the trigonometric equation:
sin(1.2217) = h / 11
Now, solve for the height (h):
h = sin(1.2217) * 11
Using a scientific calculator, find the sine of 1.2217 radians and multiply it by 11 to get the height of the cone.