For a project in her Geometry class, Chloe uses a mirror on the ground to measure the height of her school’s flagpole. She walks a distance of 8.85 meters from the flagpole, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.1 meters to the other side of the mirror, until she can see the top of the flagpole clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.15 meters. How tall is the flagpole? Round your answer to the nearest hundredth of a meter.
To find the height of the flagpole, we can use similar triangles.
Let A be the top of the flagpole, B be the bottom of the flagpole, C be the point where Chloe is standing, D be the point where the mirror is placed, and E be the point where Chloe's partner is measuring the distance.
Let x be the height of the flagpole.
From the triangle ABE, we have:
tan(θ) = x / 8.85, where θ is the angle of elevation to the top of the flagpole.
From the triangle ACD, we have:
tan(θ) = x / 1.1
Setting the two expressions for tan(θ) equal to each other, we have:
x / 8.85 = x / 1.1
8.85x = 1.1x
x = 1.1 * 8.85
x = 9.735 meters
Now, we need to add Chloe's eye level height to find the total height of the flagpole:
x + 1.15 = 9.735 + 1.15
= 10.885 meters
Therefore, the height of the flagpole is 10.89 meters.