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The figure above represents a semicircular archway over a fl
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04 Jun 2020, 08:48
04 Jun 2020, 08:48
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The figure above represents a semicircular archway over a flat street. The semicircle has a center at O and a radius of 6 feet. What is the height h, in feet, of the archway 2 feet from its center?
A. √2
B. 2
C. 3
D. 4√2
E. 6
Re: The figure above represents a semicircular archway over a fl
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04 Jun 2020, 08:48
04 Jun 2020, 08:48
Expert Reply
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Re: The figure above represents a semicircular archway over a fl
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04 Jun 2020, 09:01
04 Jun 2020, 09:01
1
Carcass wrote:
The figure above represents a semicircular archway over a flat street. The semicircle has a center at O and a radius of 6 feet. What is the height h, in feet, of the archway 2 feet from its center?
A. √2
B. 2
C. 3
D. 4√2
E. 6
Let's add the radius of 6 feet to the diagram to get:
From here, we can see the right triangle hiding within the diagram, which means we can apply the Pythagorean Theorem.
Se can write: h² + 2² = 6²
Simplify: h² + 4 = 36
So, we get: h² = 32
This means h = √32
Check the answer choices. . . √32 is not among them.
Looks like we need to simplify √32
We'll use the fact that √(xy) = (√x)(√y)
So, √32 = √[(16)(2)] = (√16)(√2) = (4)(√2) = 4√2
Check the answer choices. . . D
Answer: D
Cheers,
Brent
