Question

1. set up a proportion to find the height of the tree. round your answer to the nearest meter. please show work on your study guide! set up a proportion to find the height of the tree. image of a tree and a smaller triangle with 2.5 m, 3 m, 28 m labels 70 meters 23 meters 33 meters 50 meters

Explanation:

Step1: Define Variables

Let \( h \) be the height of the tree. The smaller triangle has height \( 2.5 \, \text{m} \) and base \( 3 \, \text{m} \), the larger triangle (with the tree) has height \( h \) and base \( 28 \, \text{m} \). Since the triangles are similar, their corresponding sides are proportional.

Step2: Set Up Proportion

The proportion is \( \frac{2.5}{3} = \frac{h}{28} \).

Step3: Solve for \( h \)

Cross - multiply: \( 3h = 2.5\times28 \). Calculate \( 2.5\times28=70 \), so \( 3h = 70 \). Then \( h=\frac{70}{3}\approx23.33\). Rounding to the nearest meter, \( h\approx23 \).

Answer:

23 meters (corresponding to the option "23 meters")