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 \(\angle BMA=\angle DMC\) and \(\angle BAM = \angle DCM=90^{\circ}\), \(\triangle ABM\sim\triangle CDM\) (by AA similarity criterion).

Step2: Set up proportion

For similar triangles \(\triangle ABM\) and \(\triangle CDM\), we have the proportion \(\frac{AB}{CD}=\frac{AM}{CM}\).
Let \(AB = h\) (height of flag - pole), \(CD = 1.5\) m (height of person), \(AM = 120\) m (distance from flag - pole to mirror), \(CM = 6\) m (distance from person to mirror).
Substituting the values into the proportion: \(\frac{h}{1.5}=\frac{120}{6}\).

Step3: Solve for \(h\)

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

Answer:

\(h = 30\) m.