The formula to calculate the hill angle (HA) is:
\[ HA = \arctan\left(\frac{H}{HD}\right) \times 57.2958 \]
Where:
Let's say the height of the hill is 10 meters, and the horizontal distance is 20 meters. Using the formula:
\[ HA = \arctan\left(\frac{10}{20}\right) \times 57.2958 \]
We get:
\[ HA = \arctan(0.5) \times 57.2958 \approx 26.57 \]
So, the hill angle (\( HA \)) is approximately 26.57 degrees.
The hill angle is the angle of inclination of a hill, calculated using the height of the hill and the horizontal distance. It is useful in various fields such as engineering, construction, and outdoor activities to understand the steepness of a slope.
Definition: Calculates the angle based on distance and height.
Formula: \( \theta = \arctan \left( \frac{\text{Height}}{\text{Distance}} \right) \)
Example: \( \theta = \arctan \left( \frac{10}{50} \right) \)
Definition: Calculates the angle given the lengths of the sides of a right triangle.
Formula: \( \theta = \arccos \left( \frac{\text{Adjacent}}{\text{Hypotenuse}} \right) \)
Example: \( \theta = \arccos \left( \frac{30}{50} \right) \)
Definition: Calculates the length of a side given an angle and another side in a right triangle.
Formula: \( \text{Opposite} = \text{Adjacent} \times \tan(\theta) \)
Example: \( \text{Opposite} = 20 \times \tan(30^\circ) \)
Definition: Calculates the angle based on the length and height of a right triangle.
Formula: \( \theta = \arctan \left( \frac{\text{Height}}{\text{Length}} \right) \)
Example: \( \theta = \arctan \left( \frac{15}{40} \right) \)
Definition: Calculates the height of a right triangle given an angle and the length of the adjacent side.
Formula: \( \text{Height} = \text{Adjacent} \times \tan(\theta) \)
Example: \( \text{Height} = 25 \times \tan(45^\circ) \)
Definition: Calculates the angle of a right triangle given the length and height.
Formula: \( \theta = \arctan \left( \frac{\text{Height}}{\text{Length}} \right) \)
Example: \( \theta = \arctan \left( \frac{12}{35} \right) \)
