(use the law of sines)
Solve triangle ABC if a=19, b=16, m<A=61
To solve triangle ABC using the law of sines, we can start by identifying the given side lengths and angle measures. In this case, we have:
a = 19
b = 16
m<A = 61°
To determine the missing side length, we can use the formula:
sin(A) / a = sin(B) / b = sin(C) / c
Since we have the measure of angle A and side a, we can rearrange the formula to solve for angle B:
sin(B) = (sin(A) * b) / a
sin(B) = (sin(61°) * 16) / 19
Now, we can use the inverse sine function (sin^(-1)) to find the value of angle B:
B = sin^(-1)((sin(61°) * 16) / 19)
Next, we can find angle C using the triangle angle sum property (180° - A - B):
C = 180° - A - B
Finally, we can use the law of sines again to find the missing side length c:
c = (sin(C) * a) / sin(A)
Now, let's substitute the given values and calculate the missing angles and side length.
A = 61°
B = sin^(-1)((sin(61°) * 16) / 19)
C = 180° - A - B
c = (sin(C) * a) / sin(A)
After evaluating these equations, we will have solved triangle ABC using the law of sines.
Firstly sinA/a = SinB/b
that is
Sin61/19 = SinB/16
and solve for B