The vertical angle of a cone is 110° and the diameter of its base is 186mm. What is its height?
To find the height of a cone, we can use the formula:
height = (radius * tan(vertical angle)) * 2
First, we need to find the radius of the base. The diameter of the base is given as 186mm, so the radius is half of that:
radius = 186mm / 2 = 93mm
Next, we can substitute the values into the formula:
height = (93mm * tan(110°)) * 2
To calculate the value of tan(110°), we can use a calculator:
tan(110°) = -0.5773 (rounded to four decimal places)
Now we can calculate the height:
height = (93mm * -0.5773) * 2
height = -59.9886mm (rounded to four decimal places)
So, the height of the cone is approximately -59.99mm. Note that the negative sign indicates that the height is in the opposite direction of the vertical angle.