Question

3.) a person is trying to find the height of a flagpole or ab. this person is 1.5 m tall and is standing at dc. a mirror is placed at point m. this mirror is 6 m away from the person and 120 m away from the flagpole. angles bma and dmc are congruent. find the height of the flagpole or ba.

Explanation:

Step1: Identify similar triangles

Since \(\angle BAM=\angle DCM = 90^{\circ}\) and \(\angle BMA=\angle DMC\), by the AA (Angle - Angle) similarity criterion, \(\triangle BMA\sim\triangle DMC\).

Step2: Set up the proportion

For similar triangles \(\triangle BMA\) and \(\triangle DMC\), the ratios of corresponding sides are equal. That is \(\frac{BA}{DC}=\frac{MA}{MC}\).
We know that \(DC = 1.5\space m\), \(MA=120\space m\), and \(MC = 6\space m\). Substituting these values into the proportion \(\frac{BA}{1.5}=\frac{120}{6}\).

Step3: Solve for \(BA\)

Cross - multiply: \(6\times BA=1.5\times120\).
First, calculate \(1.5\times120 = 180\). Then, \(BA=\frac{180}{6}\).

Answer:

\(BA = 30\space m\)