Hello! I need help with this question. I know that I'm using the Law of Sines, but I'm confused on how to solve. I have to also round my answers to the nearest tenth for degrees and to the nearest hundredth for sides. Thanks!
Given:
A = 60 degrees
a = 9
c = 10
Find:
b=
C=
B=
Sine rule states that:
sin(A)/a = sin(B)/b = sin(C)/c
Here you are given both a and A, so knowledge of c will let you solve for sin(C).
Sin(C)=c*(sin(A)/a)=0.96225
and sin-10.96225=74.207° or 105.793° since sin(x) is symmetrical about 90°.
If the sum of the larger angle (>90°, i.e. 105.793) and the known angle (60°) exceeds 180° then the larger angle can be rejected.
This is not the case in this problem, so the solution of this triangle has two solutions using the sine rule:
A=60, C=74.207, B=180-A-C
or
A=60, C=105.793, B=180-A-C.
The corresponding third side (b) can be found again using the sine rule once B is known.
To solve this problem using the Law of Sines, you can follow these steps:
Step 1: Write down the given information:
A = 60 degrees
a = 9
c = 10
Step 2: Identify the missing side or angle you need to find:
We need to find:
b (the side opposite angle B)
C (angle opposite side c)
B (angle opposite side b)
Step 3: Use the Law of Sines formula:
The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is the same for all sides and angles.
The formula is: a/sin(A) = b/sin(B) = c/sin(C)
Step 4: Plug in the given values into the formula:
9/sin(60) = b/sin(B) = 10/sin(C)
Step 5: Solve for b:
To solve for b, we rearrange the formula to isolate b.
b = (sin(B) * a) / sin(A)
b = (sin(B) * 9) / sin(60)
Step 6: Calculate b:
Using a scientific calculator, calculate the value of sin(60). Then, substitute the values of sin(60), a, and B into the formula and solve for b.
Step 7: Solve for C:
To solve for C, we can use the fact that the sum of angles in a triangle is 180 degrees.
C = 180 - A - B
Substitute the values of A and B into the formula and solve for C.
Step 8: Solve for B:
Similarly, you can solve for B using the fact that the sum of angles in a triangle is 180 degrees.
B = 180 - A - C
Substitute the values of A and C into the formula and solve for B.
Remember to round your answers to the nearest tenth for degrees and to the nearest hundredth for sides, as specified in the question.