Math Problem Statement
As shown in the diagram $\angle BAC=90^\circ$. Let $X$ be the foot of the altitude from $A$ to $\overline {BC}$, $\overline{AY}$ be the bisector of $\angle BAC$, and $\overline{AZ}$ be the median of $\triangle ABC$. If $\angle XAY = 22^\circ$, then what is the measure of $\angle ZAC$ in degrees?
Solution
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Math Problem Analysis
Mathematical Concepts
Geometry
Right Triangles
Angle Bisectors
Medians
Altitudes
Formulas
Angle bisector divides an angle into two equal parts
Median from the right-angle vertex of a triangle divides the hypotenuse into two equal segments
Theorems
Angle Bisector Theorem
Properties of Medians in Right Triangles
Altitude in Right Triangle Properties
Suitable Grade Level
Grades 9-12
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