Question

nicole is 1.55 meters tall. at 2 p.m., she measures the length of a tree’s shadow to be 30.05 meters. she stands 25.6 meters away from the tree, so that the tip of her shadow meets the tip of the tree’s shadow. find the height of the tree to the nearest hundredth of a meter. (diagram is not to scale.)

Explanation:

Step1: 确定相似三角形

因为光线平行，所以人和树的三角形相似。设树高为\(h\)，人的影长为\(30.05 - 25.6 = 4.45\)米。

Step2: 列比例式

根据相似三角形对应边成比例，\(\frac{1.55}{4.45}=\frac{h}{30.05}\)。

Step3: 求解\(h\)

交叉相乘得\(4.45h = 1.55\times30.05\)，计算右边\(1.55\times30.05 = 46.5775\)，则\(h=\frac{46.5775}{4.45}\approx10.47\)。

Answer:

\(10.47\)米