The vertical angle of a cone is 110 degree and the diametre of its base is 186mm.What is its height?
Now you do some. I already took the course.
To find the height of a cone with a given vertical angle and diameter of its base, we can use some basic trigonometry. Here's how you can calculate it:
1. Start by drawing a vertical cross-section of the cone. The vertical angle refers to the angle formed between the line through the tip of the cone and the center of its base, and the line from the base to the tip.
2. Split the cone into two right triangles by drawing a line from the tip of the cone to the center of the base. This line represents the height of the cone.
3. Since we know the vertical angle is 110 degrees, the angle formed between the height line and the base is half of the vertical angle, which is 55 degrees.
4. Next, use the trigonometric function tangent (tan) to find the ratio of the opposite side (height) to the adjacent side (radius of the base). In this case, the radius is half of the diameter.
5. Convert the diameter from millimeters to centimeters by dividing it by 10. So, the radius of the base is 186 mm / 10 = 18.6 cm.
6. Now, use the tangent function: tan(55 degrees) = height / 18.6 cm
7. Rearrange the equation to solve for the height: height = tan(55 degrees) * 18.6 cm
8. Calculate the height using a calculator or trigonometric table. The value of tan(55 degrees) is approximately 1.4281.
9. Multiply the value of tan(55 degrees) by 18.6 cm: height = 1.4281 * 18.6 cm
10. Finally, calculate the height: height ≈ 26.59 cm
Therefore, the height of the cone is approximately 26.59 cm.