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. A=35∘a=24b=19Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. There is only one possible solution for the triangle.The measurements for the remaining angles B and C and side c are as follows.B=□∘C=□∘(Round to the nearest tenth as needed.)c=□B. There are two possible solutions for the triangle.The measurements for the solution with the longer side c are as follows.B1=□∘C1=□∘B0The measurements for the solution with the shorter side c are as follows.B2B3(Round to the nearest tenth as needed.)C. There are no possible solutions for the triangle.View an exampleGet more help -Clear all
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. A=35∘a=24b=19Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. There is only one possible solution for the triangle.The measurements for the remaining angles B and C and side c are as follows.B=□∘C=□∘(Round to the nearest tenth as needed.)c=□B. There are two possible solutions for the triangle.The measurements for the solution with the longer side c are as follows.B1=□∘C1=□∘B0The measurements for the solution with the shorter side c are as follows.B2B3(Round to the nearest tenth as needed.)C. There are no possible solutions for the triangle.View an exampleGet more help -Clear all
Use Law of Sines: Use the Law of Sines to determine the possible values for angle B. The Law of Sines states that asin(A)=bsin(B). We have A=35∘, a=24, and b=19. Let's calculate sin(B).sin(B)=asin(35∘)×b=24sin(35∘)×19
Calculate sin(B): Calculate the value of sin(B) using the values from Step 1.sin(B)=(sin(35°)×19)/24≈(0.5736×19)/24≈0.4523
Determine possible angles: Determine the possible angles for B using the value of sin(B). Since sin(B) is positive and less than 1, there are two possible angles for B in the range of 0° to 180°: B and 180°−B.B≈arcsin(0.4523)sin(B)0sin(B)1
Check validity of B2: Check if the second possible angle B2 leads to a valid triangle by adding it to angle A and seeing if the sum is less than 180°.A+B2=35°+153.1°=188.1°Since the sum of angles A and B2 is greater than 180°, this combination does not lead to a valid triangle.
Find angle C: Since B2 does not lead to a valid triangle, we only have one possible angle for B, which is B1. Now we can find angle C by subtracting the sum of angles A and B1 from 180∘. C=180∘−A−B1=180∘−35∘−26.9∘≈118.1∘
Use Law of Sines again: Now that we have angles A, B1, and C, we can use the Law of Sines again to find the length of side c.csin(C)=asin(A)c=sin(A)sin(C)⋅a=sin(35∘)sin(118.1∘)⋅24
Calculate side c: Calculate the value of side c using the values from Step 6.c≈(sin(118.1∘)×24)/sin(35∘)≈(0.8716×24)/0.5736≈36.5
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