Calculating the height of a cone with circumference and angle.

Question

A hedge has been trimmed to look like a cone (Birthday party hat). The circumference of the base of the hedge is 2m. The angle between the base of the hedge and the point at the top is 75°. What is the height of the hedge?

Answer 1

I am going to assume you mean that the angle between the slanted side of the cone and the ground is 75 degrees, so the angle between the slanted side and the vertical is 5 degrees, because you can draw a triangle between the slant height of the cone, the radius of the base and the vertical (90 degree angle) from the base to the point of the cone. From the circumference you can get the radius. Circumference = 2πr = 2 meters. So radius is 2/(2pi*r). Now draw this out and look at the triangle created. The base has a length of r, and the height and hypotenuse (slant height) can be found using trigonometry. If the angle at the base is 75 degrees, what is the value of the tangent of 75 degrees on your triangle? Solve from there.