Given: b = 600, B = 11°, C = 75° in triangle ABC; find a. (Round the answer to the nearest whole number.)
a =
You know A, since A+B+C=180
a/sinA = b/sinB
...
To find the value of side a in triangle ABC, we can use the Law of Sines. According to the Law of Sines, the ratio of the length of a side to the sine of its opposing angle is the same for all sides and their opposing angles in a triangle.
The formula for the Law of Sines is as follows:
a/sin(A) = b/sin(B) = c/sin(C)
Given:
b = 600
B = 11°
C = 75°
We can substitute these values into the Law of Sines formula to find the value of side a.
a/sin(A) = 600/sin(11°)
Now, to solve for a, we need to isolate it in the equation. Multiply both sides of the equation by sin(A):
a = 600 * sin(A) / sin(11°)
To find the value of sin(A), we can use the fact that the sum of the angles in a triangle is always 180°. We already know the values of angles B and C, so we can find angle A:
A = 180° - B - C
A = 180° - 11° - 75°
A = 94°
Now we can substitute the value of A into the equation to find the value of a:
a = 600 * sin(94°) / sin(11°)
Using a calculator, we can evaluate sin(94°) and sin(11°):
a = 600 * 0.999039 / 0.190809
a = 313.566
Finally, rounding the answer to the nearest whole number, we find that a ≈ 314.