[ Pythagorean Theorem (direct and inverse). ] [ The larger angle lies opposite the larger side ]

In a triangle, the larger angle at the base is equal to $45^{\circ}$, and the height divides the base into segments of 20 and 21. Find the larger lateral side.
In a triangle, the side opposite the larger angle is the longer side.

## Solution

Let $\angle A=45^{\circ}$. Since $\angle A>\angle C$, then $B C>A B$, which means $B C$ is the longer lateral side. Therefore, $B D=A D=20, B C^{2}=B D^{2}+D C^{2}=841=29^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_9617f685748a8dfcd82ag-06.jpg?height=324&width=650&top_left_y=2219&top_left_x=704)

## Answer

29. 

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