Question

jai is 1.45 meters tall. at 11 a.m., he measures the length of a trees shadow to be 39.55 meters. he stands 34.1 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.
(diagram is not to scale.)

Explanation:

Step1: 计算Jai的影子长度

树的影子总长是39.55米，Jai离树34.1米，所以Jai的影子长度为\( 39.55 - 34.1 = 5.45 \)米。

Step2: 建立相似三角形比例关系

设树的高度为\( h \)米。因为人和树的影子形成的三角形相似，所以高度与影子长度的比相等，即\( \frac{1.45}{5.45} = \frac{h}{39.55} \)。

Step3: 求解树的高度\( h \)

根据比例关系，交叉相乘可得\( h = \frac{1.45 \times 39.55}{5.45} \)。先计算分子\( 1.45 \times 39.55 = 57.3475 \)，再除以分母\( 5.45 \)，即\( h = \frac{57.3475}{5.45} \approx 10.52 \)（米）。

Answer:

树的高度约为\( 10.52 \)米。