Given: a = 640, A = 70°, B = 52° in triangle ABC ; find c . Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrec
Angle C
180 - 70 - 52 = 58
640/sin 70 = c/sin 58
640(sin 58)/(sin 70) = c
To find c in triangle ABC, we can use the Law of Sines which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
The formula for the Law of Sines is:
a/sin(A) = b/sin(B) = c/sin(C)
In this case, we are given a = 640, A = 70°, and B = 52°. We need to find c.
Using the Law of Sines, we can set up the following equation:
640/sin(70°) = c/sin(C)
Now, let's solve for c:
1. Divide both sides of the equation by sin(70°):
c = (640 * sin(C)) / sin(70°)
In order to solve for c, we still need to find the value of sin(C). We can do this by using the fact that the sum of the angles in a triangle equals 180°.
Since we know A = 70° and B = 52°, we can find C:
C = 180° - A - B
C = 180° - 70° - 52°
C = 58°
Now we can substitute the value of C into the equation we found earlier:
c = (640 * sin(58°)) / sin(70°)
Using a scientific calculator, we can evaluate sin(58°) and sin(70°) to find the value of c.
After calculating the value of c, round it to the nearest whole number according to the given instructions. Do not use a decimal point or extra spaces in the answer.
That's how you find c in triangle ABC using the Law of Sines!
To find side c in triangle ABC, we can use the law of sines. 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 constant.
We have the following information:
a = 640
A = 70°
B = 52°
To find side c, we can use the following formula:
c/sin(C) = a/sin(A)
First, let's find angle C. Since the sum of angles in a triangle is 180°, we can find angle C using the formula:
C = 180° - A - B
C = 180° - 70° - 52°
C = 58°
Now, we can substitute the values into the formula and solve for c:
c/sin(58°) = 640/sin(70°)
To find sin(58°) and sin(70°), we can use a calculator.
sin(58°) ≈ 0.848
sin(70°) ≈ 0.939
Dividing both sides of the equation by sin(58°):
c ≈ (640 * sin(58°)) / sin(70°)
c ≈ (640 * 0.848) / 0.939
c ≈ 579.2 / 0.939
c ≈ 616.94
Rounding to the nearest whole number, c ≈ 617.
Therefore, side c is approximately 617.