For a project in her Geometry class, Nakeisha uses a mirror on the ground to measure the height of her school building. She walk
s a distance of 8.65 meters from the school, then places a mirror on flat on the ground, marked with an X at the center. She then steps 1.65 meters to the other side of the mirror, until 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 1.25 meters. How tall is the school? Round your answer to the nearest hundredth of a meter.
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1 answer:
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So with this, we will be using proportions. To solve for x, our proportion will be
Firstly, cross-multiply:
Next, subtract 36 on both sides:
Next, replace -9x with 3x-12x
Next, factor x^2+3x and -12x-36 separately: . After, rewrite it as
Next, solve for x separately in the two parentheses:
Since we can't have a negative length, x = 12.
To solve for y, our proportion will be
Firstly, cross-multiply:
Next, just square root each side, and your answer will be (rounded to hundredths)
In short, x = 12 and y = 10.39.