Question

for a project in his geometry class, anand uses a mirror on the ground to measure the height of his school’s football goalpost. he walks a distance of 14.75 meters from the goalpost, then places a mirror flat on the ground, marked with an x at the center. he then steps 1.3 meters to the other side of the mirror, until he can see the top of the goalpost clearly marked in the x. his partner measures the distance from his eyes to the ground to be 1.45 meters. how tall is the goalpost? round your answer to the nearest hundredth of a meter.

Explanation:

Step1: Identify similar triangles

The two triangles (one formed by Anand's height and his distance from the mirror, and the other formed by the goalpost's height and its distance from the mirror) are similar by the law of reflection (angle of incidence equals angle of reflection) and right angles (both Anand and the goalpost are vertical, the ground is horizontal). So, the ratios of corresponding sides are equal. Let \( h \) be the height of the goalpost. Then we have the proportion: \(\frac{h}{14.75}=\frac{1.45}{1.3}\)

Step2: Solve for \( h \)

Cross - multiply to get \( h=\frac{1.45\times14.75}{1.3}\)
First, calculate the numerator: \( 1.45\times14.75 = 1.45\times(14 + 0.75)=1.45\times14+1.45\times0.75 = 20.3+1.0875 = 21.3875\)
Then, divide by 1.3: \( h=\frac{21.3875}{1.3}\approx16.56\) (rounded to the nearest hundredth)

Answer:

16.56 meters