Question

for a project in her geometry class, hailey uses a mirror on the ground to measure the height of her school’s flagpole. she walks a distance of 11.15 meters from the flagpole, then places a mirror flat on the ground, marked with an x at the center. she then steps 1.35 meters to the other side of the mirror, until she can see the top of the flagpole 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 flagpole? round your answer to the nearest hundredth of a meter.
(diagram is not to scale.)

Explanation:

Step1: 确定相似三角形

由于光的反射定律，两个直角三角形（人的和旗杆的）相似，对应边成比例。设旗杆高度为\(h\)。
比例关系为\(\frac{h}{11.15}=\frac{1.55}{1.35}\)

Step2: 求解\(h\)

交叉相乘得\(h = \frac{1.55\times11.15}{1.35}\)
计算分子：\(1.55\times11.15 = 17.2825\)
再计算除法：\(h=\frac{17.2825}{1.35}\approx12.79\)

Answer:

\(12.79\)米