In /_\VWX,w=510 inches, v=890 inches and /_V=137^(@). Find all possible values of /_W, to the nearest degree. Answer:

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In  /_\VWX,w=510 inches,  v=890 inches and  /_V=137^(@). Find all possible values of  /_W, to the nearest degree. Answer:

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Apply Law of Sines: To find the possible values of /_W, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. The formula is given by:  a/sin(A) = b/sin(B) = c/sin(C)  where a, b, and c are the lengths of the sides, and A, B, and C are the angles opposite those sides, respectively. In our case, we have:  v/sin(V) = w/sin(W)  We can plug in the values we know to find sin(W):  890/sin(137°) = 510/sin(W)Find sin(137°): First, we need to find the value of sin(137°). Since 137° is in the second quadrant where sine is positive, we can use the fact that sin(180° - θ) = sin(θ) for angles in the second quadrant. Therefore, sin(137°) = sin(180° - 137°) = sin(43°).Calculate sin(W): Now we can solve for sin(W):  sin(W) = 510 * sin(43°) / 890  We can use a calculator to find sin(43°) and then compute sin(W):  sin(43°) ≈ 0.682 sin(W) ≈ 510 * 0.682 / 890 sin(W) ≈ 0.390Find angle W: Now that we have sin(W), we can find the angle W by taking the inverse sine (arcsin) of 0.390. However, we must consider that there could be two possible angles for W in a triangle since the sine function is positive in both the first and second quadrants. We will find the principal value (the smallest angle) first:  W ≈ arcsin(0.390) W ≈ 23° (to the nearest degree)Consider Supplementary Angle: To find the second possible value for angle W, we need to consider the supplementary angle, since sin(W) = sin(180° - W). This is because in a triangle, the sum of the angles must be 180°, and we already have one angle that is 137°. The sum of the remaining two angles must be 180° - 137° = 43°. Since we found one possible value for W to be 23°, the other value must be 43° - 23° = 20°.However, upon reviewing the last step, we realize that the second angle calculation was incorrect. Since we already have one angle of 137°, and we found W to be 23°, the third angle (angle X) would be 180° - 137° - 23° = 20°. This means that there is only one possible value for angle W, which is 23°, because the angles in a triangle must sum up to 180°, and having two different values for angle W would violate this rule. Therefore, the only possible value for angle W is 23°.

In $\triangle \mathrm{VWX}, w=510$ inches, $v=890$ inches and $\angle \mathrm{V}=137^{\circ}$ . Find all possible values of $\angle \mathrm{W}$ , to the nearest degree. $\newline$ Answer:

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In △VWX,w=510 \triangle \mathrm{VWX}, w=510 △VWX,w=510 inches, v=890 v=890 v=890 inches and ∠V=137∘ \angle \mathrm{V}=137^{\circ} ∠V=137∘. Find all possible values of ∠W \angle \mathrm{W} ∠W, to the nearest degree.\newlineAnswer:

In $\triangle \mathrm{VWX}, w=510$ inches, $v=890$ inches and $\angle \mathrm{V}=137^{\circ}$ . Find all possible values of $\angle \mathrm{W}$ , to the nearest degree. $\newline$ Answer: