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Solve the SSA triangle. Indicate whether the given measurements result in no triangle, one triangle, or two triangles. Solve each resulting triangle. Round each answer to the nearest tenth. \newlineA=35a=24b=19 A=35^\circ \quad a=24 \quad b=19 \newlineSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.\newlineA. There is only one possible solution for the triangle.\newlineThe measurements for the remaining angles \newlineB B and \newlineC C and side \newlinec c are as follows.\newlineB= B=\square^\circ \newlineC= C=\square^\circ \newline(Round to the nearest tenth as needed.)\newlinec= c=\square \newlineB. There are two possible solutions for the triangle.\newlineThe measurements for the solution with the longer side \newlinec c are as follows.\newlineB1= B_{1}=\square^\circ \newlineC1= C_{1}=\square^\circ \newlineB B 00\newlineThe measurements for the solution with the shorter side \newlinec c are as follows.\newlineB B 22\newlineB B 33\newline(Round to the nearest tenth as needed.)\newlineC. There are no possible solutions for the triangle.\newlineView an example\newlineGet more help -\newlineClear all

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Q. Solve the SSA triangle. Indicate whether the given measurements result in no triangle, one triangle, or two triangles. Solve each resulting triangle. Round each answer to the nearest tenth. \newlineA=35a=24b=19 A=35^\circ \quad a=24 \quad b=19 \newlineSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.\newlineA. There is only one possible solution for the triangle.\newlineThe measurements for the remaining angles \newlineB B and \newlineC C and side \newlinec c are as follows.\newlineB= B=\square^\circ \newlineC= C=\square^\circ \newline(Round to the nearest tenth as needed.)\newlinec= c=\square \newlineB. There are two possible solutions for the triangle.\newlineThe measurements for the solution with the longer side \newlinec c are as follows.\newlineB1= B_{1}=\square^\circ \newlineC1= C_{1}=\square^\circ \newlineB B 00\newlineThe measurements for the solution with the shorter side \newlinec c are as follows.\newlineB B 22\newlineB B 33\newline(Round to the nearest tenth as needed.)\newlineC. There are no possible solutions for the triangle.\newlineView an example\newlineGet more help -\newlineClear all
  1. Use Law of Sines: Use the Law of Sines to determine the possible values for angle BB. The Law of Sines states that sin(A)a=sin(B)b\frac{\sin(A)}{a} = \frac{\sin(B)}{b}. We have A=35A = 35^\circ, a=24a = 24, and b=19b = 19. Let's calculate sin(B)\sin(B).\newlinesin(B)=sin(35)×ba=sin(35)×1924\sin(B) = \frac{\sin(35^\circ) \times b}{a} = \frac{\sin(35^\circ) \times 19}{24}
  2. Calculate sin(B)\sin(B): Calculate the value of sin(B)\sin(B) using the values from Step 11.\newlinesin(B)=(sin(35°)×19)/24(0.5736×19)/240.4523\sin(B) = (\sin(35°) \times 19) / 24 \approx (0.5736 \times 19) / 24 \approx 0.4523
  3. Determine possible angles: Determine the possible angles for BB using the value of sin(B)\sin(B). Since sin(B)\sin(B) is positive and less than 11, there are two possible angles for BB in the range of 0° to 180°180°: BB and 180°B180° - B.\newlineBarcsin(0.4523)B \approx \arcsin(0.4523)\newlinesin(B)\sin(B)00\newlinesin(B)\sin(B)11
  4. Check validity of B2B_2: Check if the second possible angle B2B_2 leads to a valid triangle by adding it to angle AA and seeing if the sum is less than 180°180°.\newlineA+B2=35°+153.1°=188.1°A + B_2 = 35° + 153.1° = 188.1°\newlineSince the sum of angles AA and B2B_2 is greater than 180°180°, this combination does not lead to a valid triangle.
  5. Find angle C: Since B2B_2 does not lead to a valid triangle, we only have one possible angle for BB, which is B1B_1. Now we can find angle CC by subtracting the sum of angles AA and B1B_1 from 180180^\circ. \newlineC=180AB1=1803526.9118.1C = 180^\circ - A - B_1 = 180^\circ - 35^\circ - 26.9^\circ \approx 118.1^\circ
  6. Use Law of Sines again: Now that we have angles AA, B1B_1, and CC, we can use the Law of Sines again to find the length of side cc.\newlinesin(C)c=sin(A)a\frac{\sin(C)}{c} = \frac{\sin(A)}{a}\newlinec=sin(C)asin(A)=sin(118.1)24sin(35)c = \frac{\sin(C) \cdot a}{\sin(A)} = \frac{\sin(118.1^\circ) \cdot 24}{\sin(35^\circ)}
  7. Calculate side c: Calculate the value of side c using the values from Step 66.\newlinec(sin(118.1)×24)/sin(35)(0.8716×24)/0.573636.5c \approx (\sin(118.1^\circ) \times 24) / \sin(35^\circ) \approx (0.8716 \times 24) / 0.5736 \approx 36.5

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