Geometry Problem 1507: Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School.

In the figure, there is a triangle ABC with altitude AD, such that angle B is double angle DAC. If BD measures 4 and DC measures 3, find the measure of AB.

Geometry Problem 1507: Understanding Triangle Geometry: Double Angles, Altitudes, and Measurements. Difficulty Level: High School

Definitions and Suggestions

A triangle is a polygon that has three sides, three vertices, and three angles. Triangles are some of the most basic shapes in geometry and can be found in many different forms.
An angle is a figure formed by two rays, or half-lines, that have a common endpoint and extend in different directions.
An altitude of a triangle is a line segment that is drawn from a vertex of a triangle perpendicular to the opposite side or to the line containing the opposite side.
Suggestions:
The sum of the angles in a triangle is always 180 degrees, which is known as the Triangle Sum Theorem.
In a triangle, if two angles are congruent, then the sides opposite those angles are also congruent.