Using the law of sines, we found that the length of side c is approximately 6.6 units when given an angle C of 25°, an angle A of 60°, and a length of side a of 14 units
To solve for the length of side c, we can use the law of sines.
The law of sines states that for any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.
In this case, we have the angle C with a measure of 25° and the length of side c, which we need to solve for.
We also have the angle opposite side C, which is angle A with a measure of 60°, and the length of side a, which is given as 14.
Using the law of sines, we can set up the following equation:
c/sinC = a/sinA
Plugging in the values we have:
c/sin(25°) = 14/sin(60°)
To solve for c, we can cross-multiply:
c * sin(60°) = 14 * sin(25°)
Then, we divide both sides by sin(60°) to isolate c:
c = (14 * sin(25°)) / sin(60°)
Using a calculator, we can find the approximate value of sin(25°) and sin(60°).
After substituting these values, we can simplify the expression and round the final answer to the nearest tenth:
c ≈ (14 * 0.4226) / 0.866
c ≈ 6.595
Therefore, the length of side c is approximately 6.6 units.