If A=55 degrees 55 minutes and c=16, find a.
a = c*sinA = 16*sin55.92 = 13.25.
To solve for angle a in a triangle, 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 its opposite angle is constant.
Using the formula for the law of sines:
sin(A) / a = sin(C) / c
Substituting the given values:
sin(55° 55') / a = sin(C) / 16
We know that sin(55° 55') can be calculated by converting the angle into decimal degrees. In this case:
55° 55' = 55 + (55 / 60) = 55.917°
Substituting this value:
sin(55.917°) / a = sin(C) / 16
Now we need to find the value of sin(C).
Since the sum of the angles in a triangle is 180 degrees, we can find angle C using:
C = 180° - 55° - 55.917°
C ≈ 69.083°
Substituting this value:
sin(55.917°) / a = sin(69.083°) / 16
Now we can solve for a.
Multiplying both sides by a and by 16:
sin(55.917°) * 16 = sin(69.083°) * a
a = (sin(55.917°) * 16) / sin(69.083°)
Using a calculator, we can compute the values of sin(55.917°) and sin(69.083°) and perform the calculations:
a ≈ (0.8390 * 16) / 0.9392
a ≈ 14.2249 / 0.9392
a ≈ 15.1623
Therefore, the value of a is approximately 15.1623.
To find the value of angle a, we can use the Law of Cosines, which states:
c^2 = a^2 + b^2 - 2ab * cos(C)
Here, a is our unknown, b is an unknown side, c is the given side (16), and C is the given angle (55 degrees 55 minutes).
First, convert the angle from degrees and minutes to decimal degrees:
55 degrees 55 minutes = 55 + (55/60) = 55.917 degrees.
Now we can substitute the known values into the equation:
16^2 = a^2 + b^2 - 2ab * cos(55.917)
Simplifying this equation will allow us to solve for a.
Note: In this response, we have assumed that angle C is opposite side c. If angle C is actually opposite side a, you would need to rearrange the equation accordingly.