Questions: To estimate the height of a stone figure, an observer holds a small square up to her eyes and walks backward from the figure. She stops when the bottom of the figure aligns with the bottom edge of the square, and when the top of the figure aligns with the top edge of the square. Her eye level is 1.81 m from the ground. She is 4.20 m from the figure. What is the height of the figure to the nearest hundredth of a meter? The height of the figure is approximately m . (Type an integer or decimal rounded to the nearest hundredth as needed.)

Solution Steps

The observer uses a small square to align the top and bottom edges of the figure with the top and bottom edges of the square. The observer's eye level is 1.81 meters from the ground, and she is 4.20 meters away from the figure. We need to find the height of the figure.

Since the observer's eye level and the distance from the figure form a right triangle, we can use similar triangles to set up a proportion. The height of the figure (H) and the distance from the observer to the figure (4.20 m) form one triangle, and the observer's eye level (1.81 m) and the same distance (4.20 m) form another triangle.

The triangles are similar, so the ratios of their corresponding sides are equal: \[ \frac{H}{4.20} = \frac{1.81}{4.20} \]

To find the height of the figure, solve the proportion: \[ H = \frac{1.81}{4.20} \times 4.20 \] \[ H = 1.81 \]

Final Answer