Which trigonometric function is typically used to find the angle of elevation from a point on the ground to the top of a building when the height of the building $h$ and the horizontal distance from the building $d$ are known?

• A. $\sin$
• B. $\cot$
• C. $\tan$
• D. $\cos$

Answer: (C)

Verified step by step guidance

1. Identify the right triangle formed by the building height, the horizontal distance, and the line of sight from the point on the ground to the top of the building.
2. Recognize that the angle of elevation is the angle between the horizontal distance and the line of sight.
3. Recall the definitions of the primary trigonometric functions in a right triangle: \(\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}\), and \(\tan \theta = \frac{\text{opposite}}{\text{adjacent}}\).
4. Since the height of the building corresponds to the side opposite the angle of elevation and the horizontal distance corresponds to the adjacent side, use the tangent function: \(\tan \theta = \frac{h}{d}\).
5. Therefore, to find the angle of elevation \(\theta\), you would use the inverse tangent function: \(\theta = \tan^{-1} \left( \frac{h}{d} \right)\).