 balloon is connected to a meteorological station by a cable of length 200 m inclined at 60 degree angle . Find the  height of the balloon from the ground. 

To find the height of the balloon from the ground, we can use trigonometry. The situation forms a right triangle, where:

- The cable is the hypotenuse (\( c = 200 \) m).
- The angle between the cable and the ground is \( 60^\circ \).
- The height of the balloon (\( h \)) is the side opposite to the angle.

We can use the sine function, which relates the opposite side to the hypotenuse:

\[
\sin(60^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{200}
\]

Now, solve for \( h \):

\[
h = 200 \times \sin(60^\circ)
\]

Since \(\sin(60^\circ) = \frac{\sqrt{3}}{2}\), we have:

\[
h = 200 \times \frac{\sqrt{3}}{2}
\]

\[
h = 100\sqrt{3} \approx 173.21 \, \text{m}
\]

So, the height of the balloon from the ground is approximately **173.21 meters**.

Would you like more details or have any questions? Here are some related problems:

1. What is the horizontal distance between the station and the balloon?
2. How would the height change if the angle were 45 degrees instead of 60 degrees?
3. If the cable length were increased to 300 m, what would be the new height?
4. How do you find the angle if the height and cable length are known?
5. What trigonometric function would you use if you knew the height and horizontal distance?

**Tip:** Always sketch a triangle to visualize trigonometric problems—it makes it easier to identify the correct function to use!

balloon is connected to a meteorological station by a cable of length 200 m inclined at 60 degree angle. Find the height of the balloon from the ground.

Learn how to calculate the height of a balloon from the ground using a 200-meter cable inclined at a 60-degree angle with trigonometric principles. This problem uses the sine function to find the height and is suitable for students in Grades 9-10. Includes step-by-step calculations and related problems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation