Із заданої точки до площини проведено перпендикуляр і похилу. Довжина перпендикуляра дорівнює проєкції похилої. Знайди кут між перпендикуляром і похилою.

1. Break Down the Problem

1. Identify the relationship between the perpendicular and the inclined line (похилою).
2. Understand that we need to find the angle between the perpendicular and the inclined line.
3. Use the given information that the length of the perpendicular is equal to the projection of the inclined line onto the perpendicular.

2. Relevant Concepts

1. Let $P$ be the length of the perpendicular.
2. Let $L$ be the length of the inclined line (похилою).
3. The projection of the inclined line onto the perpendicular can be expressed as: $\text{Projection} = L \cdot \cos(\theta)$ where $\theta$ is the angle between the inclined line and the perpendicular.

3. Analysis and Detail

1. Given that $P = L \cdot \cos(\theta)$.
2. Rearranging gives us: $\cos(\theta) = \frac{P}{L}$
3. To find the angle $\theta$, we can use the inverse cosine: $\theta = \cos^{-1}\left(\frac{P}{L}\right)$

4. Verify and Summarize

• Since $P$ is equal to the length of the perpendicular, we can determine $\theta$ by knowing the values of $P$ and $L$.
• If we have specific values for $P$ and $L$, we can compute an exact numerical value for $\theta$.

Final Answer

The angle $\theta$ between the perpendicular and the inclined line can be expressed as: $\theta = \cos^{-1}\left(\frac{P}{L}\right)$ If additional specifics were provided regarding lengths $P$ and $L$, the angle could be calculated numerically.