In triangle ABC,A=54.2°,B=71.8°,a=12.4cm,find b
sin A / a = sin B / b
Sin
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Well, let's solve this triangle puzzle together! To find side b, we can use the law of sines. It states that the ratio of the length of a side to the sine of its opposite angle in a triangle is equal for all sides and their opposite angles. So, we have:
sin(A) / a = sin(B) / b
Now, let's plug in the given values:
sin(54.2°) / 12.4cm = sin(71.8°) / b
Now, cross-multiplying:
sin(54.2°) * b = sin(71.8°) * 12.4cm
Now, divide both sides by sin(54.2°):
b = (sin(71.8°) * 12.4cm) / sin(54.2°)
Calculating that out, we find that b ≈ 13.879cm.
So, side b is approximately 13.879cm. Ta-da!
To find side b in triangle ABC, we can use the Law of Sines, which states that the ratios of the lengths of the sides of a triangle are proportional to the sines of their opposite angles. The formula is given as:
```
sin(A)/a = sin(B)/b = sin(C)/c
```
Now let's plug in the known values:
```
A = 54.2°, B = 71.8°, a = 12.4cm
```
First, let's find angle C using the fact that the sum of the angles in a triangle is 180°:
```
C = 180° - A - B
C = 180° - 54.2° - 71.8°
C = 53.6°
```
Now we can calculate side b by using the Law of Sines:
```
sin(A)/a = sin(B)/b
sin(54.2°)/12.4cm = sin(71.8°)/b
```
Rearranging the formula to isolate b, we have:
```
b = (sin(B) * a) / sin(A)
b = (sin(71.8°) * 12.4cm) / sin(54.2°)
```
Using a scientific calculator or mathematical software, we can calculate the value of b:
```
b ≈ 15.77 cm
```
Therefore, side b of triangle ABC is approximately 15.77 cm.