In the given diagram, angle $\hat{A} = 40^\circ$ represents the angle at point $A$. This angle is formed between the horizontal line (along the base $AB$) and the cable line $AC$, which leads up to point $C$.

This angle $\hat{A}$ is known as the angle of elevation of point $C$ from point $A$. The angle of elevation is defined as the angle formed by the horizontal and the line of sight from an observer to a point above the horizontal level, which in this case is the top of the mountain at point $C$. Hence, the elevation angle of $C$ from $A$ is $40^\circ$.

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5 Relative Questions:

1. How would you calculate the height $h$ of the mountain using trigonometry?
2. What trigonometric function is related to the angle of elevation and the height of the mountain in this scenario?
3. If the angle of elevation was increased, how would it affect the height of the mountain?
4. What is the formula to calculate the horizontal distance $AB$ using the given information?
5. How can the concept of a right triangle be applied in other real-life elevation problems?

Tip:

When dealing with right triangles, always identify the known sides or angles first to determine which trigonometric functions (sine, cosine, tangent) to use for your calculations.