# Geometry Problem 1548: Exploring Segment DE Length in Triangle ABC with a 45-Degree Angle and Intersecting Altitudes: A High School and College Level Investigation

Given a triangle ABC with angle A measuring 45 degrees, altitudes BD and CE intersect at point F. If the distance from vertex A to segment DE is 36 units and the distance from point F to segment DE is 6 units, find the length of segment DE.

Triangle's 45,

Altitudes, heights converge bright,

Given lengths in sight,

Seeking DE's mystery,

Distance guides, answers ignite.

## Lines and Shadows: Exploring Problem 1548 with the The Temple of the
Moon at Machu Picchu as the Backdrop

### Amid peaks it soars,

Temple
of the Moon stands tall,

Triangle's length speaks.

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## Discover Even More: See Also...

### Problem 1549

### Problem 1547

### Problem 1546

### Problem 1545

### Problem 1544