Find c , given that a = 18.2, B = 62°, and C = 48°. Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect.
c = a0
To find c, we can use the Law of Sines, which 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 three sides. In other words:
a/sin(A) = b/sin(B) = c/sin(C)
In this case, we are given a=18.2, B=62°, and C=48°. We need to find c.
We can rearrange the formula to solve for c:
c = a * sin(C) / sin(A)
To find sin(C) and sin(A), we can use a calculator or a trigonometric table. For sin(48°), the value is approximately 0.7431. For that sin(62°), the value is approximately 0.8804.
Now we can substitute the values into the formula:
c = 18.2 * 0.7431 / 0.8804
Evaluating the right side of the equation:
c ≈ 15.34
Finally, rounding to the nearest whole number:
c ≈ 15
Therefore, c is approximately 15 when rounded to the nearest whole number.
To find c, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio between the length of a side and the sine of its opposite angle is constant.
In this case, we have the following information:
a = 18.2
B = 62°
C = 48°
To find c, we can use the formula:
c / sin(C) = a / sin(A)
First, we need to find angle A. Since the sum of angles in a triangle is 180°, we can find angle A by subtracting the sum of B and C from 180°:
A = 180° - (B + C)
= 180° - (62° + 48°)
= 70°
Now, we can substitute the given values into the formula:
c / sin(48°) = 18.2 / sin(70°)
Next, we can isolate c by multiplying both sides of the equation by sin(48°):
c = (18.2 * sin(48°)) / sin(70°)
Using a calculator, we can find that sin(48°) is approximately 0.7431 and sin(70°) is approximately 0.9397. Substituting these values into the equation:
c = (18.2 * 0.7431) / 0.9397
= 14.46742 / 0.9397
≈ 15.40
Rounding to the nearest whole number, c is approximately 15.
Therefore, c ≈ 15.
since A+B+C=180, A=70°
Now use the law of sines to find c:
c/sinC = a/sinA
c/sin48° = 18.2/sin70°
c = 14.4