Find the length of side b to the nearest whole number if side a=105,angle A=65 degrees and angle B=37 degrees?
law of sines:
b/SinB=a/SinA
To find the length of side b, we can use the Law of Sines. The Law of Sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is equal to the same ratio for the other sides and their respective opposite angles.
In this case, we have side a = 105, angle A = 65 degrees, and angle B = 37 degrees. Let's denote side b as x.
Using the Law of Sines, we can set up the following proportion:
sin(A) / a = sin(B) / b
Plugging in the given values:
sin(65°) / 105 = sin(37°) / x
Now, we can solve for x:
x = (105 * sin(37°)) / sin(65°)
Using a calculator:
x ≈ 63.9 (rounded to one decimal place)
To find the length of side b to the nearest whole number, we round 63.9 to the nearest whole number:
x ≈ 64
Therefore, the length of side b, to the nearest whole number, is 64.