Question

for a project in her geometry class, addison uses a mirror on the ground to measure the height of her schools football goalpost. she walks a distance of 13.25 meters from the goalpost, then places a mirror flat on the ground, marked with an x at the center. she then steps 1.3 meters to the other side of the mirror, until she can see the top of the goalpost clearly marked in the x. her partner measures the distance from her eyes to the ground to be 1.55 meters. how tall is the goalpost? round your answer to the nearest hundredth of a meter.

Explanation:

Step1: Set up proportion

Since the two triangles are similar (by the AA similarity criterion as the angles of incidence and reflection are equal and both have right angles), we can set up the proportion \(\frac{\text{height of Addison}}{\text{her distance from mirror}}=\frac{\text{height of goalpost}}{\text{goalpost's distance from mirror}}\). Let \(h\) be the height of the goalpost. So, \(\frac{1.55}{1.3}=\frac{h}{13.25}\).

Step2: Solve for \(h\)

Cross - multiply: \(1.3h = 1.55\times13.25\). First, calculate \(1.55\times13.25=20.5375\). Then, \(h=\frac{20.5375}{1.3}\).

Step3: Calculate the value of \(h\)

\(h=\frac{20.5375}{1.3}=15.80\) (rounded to the nearest hundredth).

Answer:

\(15.80\) meters