A=30 degrees, a=9 and b=8. Find the missing sides/angles. I did cos39=x/8 and reduced that to 8cos39=x. I got 6.92. But that's not a valid answer, so I can't go from there. What did I do wrong? Can you show me how to get the other answers as well, please?
Law of sines:
a/SinA = b/SinB
solve for B from that.
Then
solve for C knowing A and B, and the sum of angles is 180
Then, find c with the law of sines, or law of cosines.
If the sine of an angle is 3/5 and the angle is not in quadrant 1, what are the remaining five trigonometric values for that angle?
To find the missing sides and angles, you can use the Law of Cosines. However, there seems to be a mistake in your calculation. Let's go through the steps together:
Given information:
A = 30 degrees, a = 9, and b = 8.
Using the Law of Cosines, we have:
c² = a² + b² − 2abcos(C)
Now we can substitute the given values:
c² = 9² + 8² − 2(9)(8)cos(C)
c² = 81 + 64 − 144cos(C)
c² = 145 − 144cos(C)
Since we are looking for side c, we will use the value of angle A (30 degrees) to find cos(C).
cos(C) = cos(180 degrees − A)
cos(C) = cos(150 degrees)
cos(C) = −√3/2 (Note: Cosine is negative in the 2nd quadrant)
Now we can substitute cos(C) into the equation:
c² = 145 − 144(−√3/2)
c² = 145 + 72√3
c ≈ √(145 + 72√3)
c ≈ 13.41 (degrees rounded to two decimal places)
To find the missing angle B, we can use the Law of Sines:
sin(B)/b = sin(A)/a
Now, substitute the known values:
sin(B)/8 = sin(30 degrees)/9
Next, cross-multiply and solve for sin(B):
sin(B) = (8)(sin(30 degrees))/9
sin(B) ≈ 0.4305
To find angle B, you can use the inverse sine function (sin^−1):
B = sin^−1(0.4305)
B ≈ 25.26 degrees (rounded to two decimal places)
To find the remaining angle C, use the fact that the sum of angles in a triangle is 180 degrees:
C = 180 − A − B
C ≈ 180 − 30 − 25.26
C ≈ 124.74 degrees (rounded to two decimal places)
Summarizing the results:
Side c ≈ 13.41
Angle B ≈ 25.26 degrees
Angle C ≈ 124.74 degrees
I hope this clarifies the process for finding the missing sides and angles.
To find the missing sides/angles in a triangle, we can use the Law of Cosines. Let's go step by step to solve the problem.
Given:
A = 30 degrees
a = 9
b = 8
To find angle B, we can use the Law of Sines:
sin B / b = sin A / a
Plugging in the values:
sin B / 8 = sin 30 / 9
Now, cross multiply and solve for sin B:
sin B = (8 * sin 30) / 9
sin B = (8 * 0.5) / 9
sin B = 0.4444
Using the inverse sine function, we can find angle B:
B ≈ arcsin(0.4444)
B ≈ 26.7 degrees
Now, to find angle C, we know that the sum of angles in a triangle equals 180 degrees:
C = 180 - A - B
C = 180 - 30 - 26.7
C ≈ 123.3 degrees
To find side c, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos C
Plugging in the values:
c^2 = 9^2 + 8^2 - 2 * 9 * 8 * cos 123.3
Now, we solve for c:
c ≈ √(81 + 64 - 144 * cos 123.3)
c ≈ √(145 + 144 * cos 123.3)
Calculating:
c ≈ √(145 + 144 * (-0.6644))
c ≈ √(145 - 95.5)
c ≈ √49.5
c ≈ 7.04
So, the missing side c is approximately 7.04.
To summarize:
Angle B is approximately 26.7 degrees.
Angle C is approximately 123.3 degrees.
Side c is approximately 7.04.
I hope this helps! Let me know if you have any further questions.