find the length of side b ABC to the nearest whole number if A = 42, B = 87, and a = 24
To find the length of side b in triangle ABC, you 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.
In this case, we have angle A equal to 42 degrees, angle B equal to 87 degrees, and side a equal to 24 units. We want to find the length of side b.
First, we need to find the sine of angle A. To do this, we can use a scientific calculator or mathematical software. The sine of an angle is the ratio of the length of the side opposite the angle to the hypotenuse. In this case, the side opposite angle A is side b and the hypotenuse is side a. So, the sine of angle A is calculated as:
sin(A) = b / a
Rearranging the formula, we can solve for b:
b = a * sin(A)
Now, we can substitute the given values into the formula:
b = 24 * sin(42)
Using a scientific calculator or mathematical software, we find that sin(42) is approximately 0.6691306064. Therefore, the length of side b is:
b ≈ 24 * 0.6691306064 ≈ 16.0571374756
Rounding this value to the nearest whole number, side b is approximately equal to 16 units.
Remember the law of sines?
a/sinA = b/sinB
24/sin42° = b/sin87°
Now you can find b with no trouble.