Given triangle ABC with a = 16, b = 14, and Angle is = 54°, find the value of c.
A. 3.1 and 20
B. 4.1 and 15
C. 15
D. 3.1
Which angle is 54° ?
â = 54°
To find the value of c in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c and angle C opposite side c, the following equation holds:
c^2 = a^2 + b^2 - 2ab * cos(C)
Let's substitute the given values into the equation:
c^2 = 16^2 + 14^2 - 2 * 16 * 14 * cos(54°)
Now we can calculate the value of c using a calculator:
c^2 = 256 + 196 - 2 * 16 * 14 * 0.5878
c^2 = 452.23
Taking the square root of both sides, we find:
c ≈ 21.27
Since none of the given answer choices match this value, there may be an error in the question or the answer choices provided. Please double-check the question and available answer choices.