Subjects trigonometry

Angle Depression

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Angle Depression


1. The problem states that the angle of depression from the top of a building to a point P on the ground is 23.6°. 2. We want to find the horizontal distance from the foot of the building to point P, assuming the height of the building is known or can be denoted as $h$. 3. Let the height of the building be $h$ and the distance from the foot of the building to point P be $d$. 4. The angle of depression is the angle formed by the horizontal from the top of the building to point P. 5. Considering the right triangle formed by the building height, the horizontal distance $d$, and the line of sight to P, we use the tangent function: $$\tan(23.6^\circ) = \frac{h}{d}$$ 6. Rearranging to solve for $d$: $$d = \frac{h}{\tan(23.6^\circ)}$$ 7. This formula gives the horizontal distance from the building to point P in terms of the building's height $h$. Final answer: $$d = \frac{h}{\tan(23.6^\circ)}$$