Question

for a project in her geometry class, janelys uses a mirror on the ground to measure the height of her school building. she walks a distance of 6.35 meters from the building, then places a mirror flat on the ground, marked with an x at the center. she then walks 3.6 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the school clearly marked in the x. her partner measures the distance from her eyes to the ground to be 1.55 meters. how tall is the school? round your answer to the nearest hundredth of a meter.

Answer 1

The height of the school is calculated using the properties of similar triangles, assuming the mirror created two similar triangles with Janelys's eye level and the height of the building. By cross-multiplying and solving the proportions, the school's height is found to be 2.71 meters.

Step-by-step explanation:

To find the height of the school using the mirror method, we need to treat the scenario as a similar triangles problem. Since Janelys can see the top of the school in the mirror, the angle of incidence equals the angle of reflection, creating two similar triangles:

Triangle formed by the height of Janelys's eyes to the ground (1.55 m), the distance between her eyes and the mirror (3.6 m), and the line of sight in the mirror.

Triangle formed by the height of the school, the distance from the school to the mirror (6.35 m), and the reflected line of sight in the mirror.

Let's denote the height of the school as 'H'. Using the properties of similar triangles:

(Height of Janelys's eyes) / (Distance of Janelys from the mirror) = (Height of the school) / (Distance of the school from the mirror)

1.55 / 3.6 = H / 6.35

By cross-multiplying and solving for H, we get:

H = (1.55 * 6.35) / 3.6

H = 2.71458 meters

Rounded to the nearest hundredth, the school is 2.71 meters tall.

Answer 2

Using the principles of similar triangles and reflection, Janelys can determine the height of the school to be approximately 2.75 meters by creating a proportion between the distances measured and her own eye level.

Step-by-step explanation:

Geometry Problem Solution:

Janelys uses the principles of similar triangles and the law of reflection to measure the height of her school building. This is a geometric method that relies on the fact that when light reflects off a surface, the angle of incidence is equal to the angle of reflection.

By placing the mirror on the ground and viewing the top of the building from a certain distance, she creates two similar triangles - one with her eye, the point where the top of the building's image appears in the mirror, and the top of the building, and the other with her eye, the mirror, and the point on the ground directly below the top of the building.

To find the height of the school, we can set up the following proportion based on the similar triangles:
(Height of School) / (Distance from Mirror to Building) = (Height of Janelys's Eyes) / (Distance from Mirror to Janelys's Eyes)
Plugging in the known distances and height, we have:
(Height of School) / 6.35 m = 1.55 m / 3.6 m

Solving for the height of the school, we find:
Height of School = (1.55 m * 6.35 m) / 3.6 m
Height of School ≈ 2.75 m
Thus, the school building is approximately 2.75 meters tall.