The vertical angle of a cone is 70% and the slant height is 11 .. calculate the height of the cone
Pls I need this answer now
To calculate the height of the cone, we can use the trigonometric relationship between the slant height, vertical angle, and height.
The vertical angle of a cone is the angle formed between the slant height and the height. In this case, the vertical angle is given as 70%. To calculate the height, we need to find the length of the side opposite to the vertical angle, which is the height of the cone.
Let's start by converting the given vertical angle from a percentage to degrees. Since there are 360 degrees in a circle, 100% represents a complete circle, which means 70% is equal to 0.7 times 360 degrees.
Vertical angle = 0.7 * 360 = 252 degrees
Now, we can use the sine function to calculate the height of the cone.
sin(vertical angle) = height / slant height
Substituting the known values:
sin(252 degrees) = height / 11
To solve for the height, we need to find the inverse sine of both sides of the equation:
height = sin^-1(sin(252 degrees)) * 11
Using a calculator, find the inverse sine of sin(252 degrees) and multiply it by 11:
height ≈ sin^-1(0.6946) * 11
height ≈ 45.8 * 11
height ≈ 503.8
Therefore, the height of the cone is approximately 503.8 units.
draw a diagram. You can see that
h/11 = sin70°
h = 65.8