Questions: Calcule x, em grau, sabendo que A H é a altura relativa ao lado B C.

Solution Steps

We are given a triangle \( \triangle ABC \) with \( \angle B = 56^\circ \) and \( AH \) as the altitude from \( A \) to \( BC \). We need to find the angle \( \angle BAC = x \).

Since \( AH \) is the altitude, it creates two right triangles: \( \triangle ABH \) and \( \triangle AHC \).

In \( \triangle ABC \), the sum of the angles is \( 180^\circ \). Therefore: \[ \angle BAC + \angle ABC + \angle ACB = 180^\circ \]

Since \( AH \) is the altitude, \( \angle AHB = 90^\circ \) and \( \angle AHC = 90^\circ \). This means: \[ \angle BAC = x \] \[ \angle ABC = 56^\circ \] \[ \angle ACB = 90^\circ - \angle BAC \]

Using the sum of angles in \( \triangle ABC \): \[ x + 56^\circ + (90^\circ - x) = 180^\circ \] \[ x + 56^\circ + 90^\circ - x = 180^\circ \] \[ 146^\circ = 180^\circ \] \[ x = 180^\circ - 146^\circ \] \[ x = 34^\circ \]

Final Answer