Given that TV ≈ TU, the inequality relating WV and WU is (A) WV > WU.
How to write inequality?
Since TV ≈ TU, this implies that the distance between T and V is approximately equal to the distance between T and U. Additionally, WU is the distance between W and U.
To relate WV and WU, consider a right triangle with vertices W, V, and U. By the Pythagorean theorem:
WV² = WU² + VU²
Since TV ≈ TU, approximate VU ≈ TU. Therefore, substitute TU for VU in the equation above:
WV² = WU² + TU²
Since TV ≈ TU, this implies that TU is slightly less than TV. Therefore, approximate TU < TV. Plugging this into the equation above:
WV² > WU² + TU²
Taking the square root of both sides:
WV > √(WU² + TU²)
Since TU < TV, simplify the equation above:
WV > WU
Therefore, the answer is (A) WV > WU.
This is the complete question:
Given that TV ≈ TU, write an inequality relating WV and WU.
A) WV > WU
B) WV < WU
C) WV = WU
D) WV + WU
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