Find the length of side b to the nearest whole number if side a =
105, angle A = 65 degrees, and angle B = 37 degree.
since the angles add to 180°, C=78°
using the law of cosines,
b/sinB = a/sinA
b/sin37° = 105/sin78°
b = .6018 * 105/.9781
b = 64.60 = 65
To find the length of side b, 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 the angle opposite that side is constant. The formula for the Law of Sines is:
a/sin(A) = b/sin(B) = c/sin(C)
In this case, we know side a and angle A, so we can rearrange the formula to solve for side b:
b = (a * sin(B)) / sin(A)
Let's plug in the values:
a = 105
A = 65 degrees
B = 37 degrees
First, let's convert the angles from degrees to radians, as most trigonometry functions work with radians:
A (in radians) = 65 * (pi/180)
B (in radians) = 37 * (pi/180)
Now we can substitute these values into the formula:
b = (105 * sin(37 * (pi/180))) / sin(65 * (pi/180))
To find the value of b, we need to evaluate the trigonometric functions sin(37 * (pi/180)) and sin(65 * (pi/180)). After substituting these values into the formula and evaluating, we get:
b ≈ 70
So, the length of side b, to the nearest whole number, is 70.