Question

travis is 1.55 meters tall. at 10 a.m., he measures the length of a trees shadow to be 21.15 meters. he stands 16.8 meters away from the tree, so that the tip of his shadow meets the tip of the trees shadow. find the height of the tree to the nearest hundredth of a meter.

Explanation:

Step1: 确定相似三角形

Travis和树分别与各自的影子构成相似三角形，因为太阳光线平行，所以两个三角形相似。设树高为\(h\)米，Travis的影子长度为\(21.15 - 16.8 = 4.35\)米。

Step2: 建立比例关系

根据相似三角形的性质，对应边成比例，即\(\frac{h}{21.15}=\frac{1.55}{4.35}\)。

Step3: 求解树高\(h\)

交叉相乘得\(h=\frac{1.55\times21.15}{4.35}\)，先计算分子\(1.55\times21.15 = 32.7825\)，再除以\(4.35\)，\(h=\frac{32.7825}{4.35}\approx7.54\)。

Answer:

树的高度约为\(7.54\)米。