In ΔVWX, the measure of ∠X=90°, XW = 48, WV = 73, and VX = 55. What is the value of the sine of ∠W to the nearest hundredth?

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hpuebla31 hpuebla31

10-09-2022
Mathematics

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In ΔVWX, the measure of ∠X=90°, XW = 48, WV = 73, and VX = 55. What is the value of the sine of ∠W to the nearest hundredth?

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sangers1959 sangers1959 · Answer 1 · 2022-09-11T00:14:02-04:00

Answer: sinW≈0.75

Step-by-step explanation:

[tex]m\angle X=90^0\ \ \ \ XV=48\ \ \ \ \ WV=73\ \ \ \ \ VX=55\ \ \ \ sinW=?[/tex]

The sine theorem: The sides of a triangle are proportional to the sines of the opposing angles

Hence,

[tex]\displaystyle\\\frac{WV}{sinX} =\frac{VX}{sinW} \\\\\frac{73}{sin90^0} =\frac{55}{sinW} \\\\\frac{73}{1} =\frac{55}{sinW} \\\\sinW=\frac{55}{73} \\\\sinW\approx0.75[/tex]