Question

For a project in her Geometry class, Kylie uses a mirror on the ground to measure

the height of her school's football goalpost. She walks a distance of 13.55 meters
from the goalpost, then places a mirror on flat on the ground, marked with an X
at the center. She then steps 1.25 meters to the other side of the mirror, until she
can see the top of the goalpost 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 goalpost?
Round your answer to the nearest hundredth of a meter.

Answer 1

To find the height of the goalpost, use similar triangles. The height is approximately 0.54 meters.

Step-by-step explanation:

To find the height of the goalpost, we can use similar triangles.

Let's label the height of the goalpost as 'h' meters. According to the given information, the height from Kylie's eyes to the ground is 1.55 meters, and she walks a distance of 13.55 meters from the goalpost.

Using the property of similar triangles, we can set up the ratio:

(h - 0.13) / 1.55 = h / 1.25

Cross multiplying gives us:

(h - 0.13) * 1.25 = h * 1.55

Simplifying the equation, we get:

1.25h - 0.1625 = 1.55h

0.3h = 0.1625

h = 0.1625 / 0.3

h ≈ 0.542 m

Rounding to the nearest hundredth, the height of the goalpost is approximately 0.54 meters.