In triangle ABC,A=38degree18',a=252m,b=198m.slove the triangle completely.With the use of sine rule
Need the calculation
sin(B) / sin(A) = b / a
C = 180º - A - B
c = b * sin(C) / sin(B)
Please help me out of this question
To solve the triangle completely using the Sine Rule, we need to find the remaining angles and sides of the triangle (B, C, b, c). The Sine Rule states:
a/sin(A) = b/sin(B) = c/sin(C)
Let's start by finding angle B:
Step 1: Convert the given angle A from degrees and minutes to decimal degrees.
A = 38° + 18'/60 = 38.3°
Step 2: Use the Sine Rule to find angle B.
a/sin(A) = b/sin(B)
252/sin(38.3°) = 198/sin(B)
To find the value of sin(B), cross multiply and solve for sin(B):
sin(B) = (198 * sin(38.3°)) / 252
B = arcsin[(198 * sin(38.3°)) / 252]
Now that we have angle B, we can find angle C:
C = 180° - A - B
Next, let's find side c:
c/sin(C) = a/sin(A)
c = (a * sin(C)) / sin(A)
Finally, we can find side b using the Sine Rule:
b/sin(B) = a/sin(A)
Now we have solved the triangle completely using the Sine Rule.