In DeltaGHI,g=9.8cm,i=9.6cm and /_I=43^(@). Find all possible values of /_G, to the nearest 10th of a degree. Answer:

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In  DeltaGHI,g=9.8cm,i=9.6cm and  /_I=43^(@). Find all possible values of  /_G, to the nearest 10th of a degree. Answer:

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Law of Sines Formula: To find the possible values of angle G, 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 opposite angle is constant for all three sides and angles in the triangle. The formula is:  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 opposite angles. In our case, we have:  g/sin(G) = i/sin(I)  We can plug in the values we know to find sin(G):  9.8/sin(G) = 9.6/sin(43 degrees)  First, we calculate sin(43 degrees):  sin(43 degrees) ≈ 0.682  Now we can solve for sin(G):  sin(G) = 9.8 * sin(43 degrees) / 9.6  sin(G) ≈ 9.8 * 0.682 / 9.6  sin(G) ≈ 6.6884 / 9.6  sin(G) ≈ 0.6967Calculating sin(G): Now that we have the value of sin(G), we can find angle G by taking the inverse sine (arcsin) of sin(G). However, since the sine function is positive in both the first and second quadrants, there are two possible angles for G that have the same sine value. These angles are supplementary, meaning they add up to 180 degrees. We will find the first angle, which is the acute angle:  G ≈ arcsin(0.6967)  G ≈ 44.4 degrees (to the nearest tenth)Finding Angle G: To find the second possible value for angle G, we subtract the first value from 180 degrees:  180 degrees - 44.4 degrees = 135.6 degrees  So the second possible value for angle G is 135.6 degrees (to the nearest tenth).Checking Validity: We must now check if the second possible value for angle G is valid by ensuring that the sum of angles in a triangle is 180 degrees. We already have angle I as 43 degrees, and we need to check if angle H can be a positive acute angle when angle G is 135.6 degrees.  Sum of angles in a triangle = 180 degrees  Angle H = 180 degrees - Angle G - Angle I  Angle H = 180 degrees - 135.6 degrees - 43 degrees  Angle H = 1.4 degrees  Since angle H is positive and less than 180 degrees, the second value for angle G is valid.

In $\Delta \mathrm{GHI}, g=9.8 \mathrm{~cm}, i=9.6 \mathrm{~cm}$ and $\angle \mathrm{I}=43^{\circ}$ . Find all possible values of $\angle \mathrm{G}$ , to the nearest $10$ th of a degree. $\newline$ Answer:

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In $\Delta \mathrm{GHI}, g=9.8 \mathrm{~cm}, i=9.6 \mathrm{~cm}$ and $\angle \mathrm{I}=43^{\circ}$ . Find all possible values of $\angle \mathrm{G}$ , to the nearest $10$ th of a degree. $\newline$ Answer: