Triangle ABC has the following non-dimension side an equals 22 cm side B equals 8.5 cm angle C equals 21. What is the length of side C
law of cosines
c^2 = a^2 + b^2 - 2 a b cos C
c^2 = 484 + 72.25 - 374 * .933 = 210
c = 14.5
To find the length of side C in triangle ABC, you can use the Law of Cosines. The formula for the Law of Cosines is c^2 = a^2 + b^2 - 2ab * cos(C), where c is the side opposite to angle C.
Given:
Side a = 22 cm
Side b = 8.5 cm
Angle C = 21 degrees
Using the Law of Cosines, we can calculate the length of side C as follows:
c^2 = a^2 + b^2 - 2ab * cos(C)
c^2 = 22^2 + 8.5^2 - 2(22)(8.5) * cos(21)
c^2 = 484 + 72.25 - 374 * cos(21)
Now, calculate cos(21) using a scientific calculator or online tool.
c^2 = 556.25 - 374 * 0.92718387
c^2 = 556.25 - 346.70633
c^2 = 209.54367
c ≈ √209.54367
c ≈ 14.486 cm
Therefore, the approximate length of side C in triangle ABC is 14.486 cm.
To find the length of side C in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice the product of those two sides multiplied by the cosine of the included angle.
In this case, we have side A = 22 cm, side B = 8.5 cm, and angle C = 21 degrees. Let's assume side C as the unknown value we want to find.
The Law of Cosines formula is as follows:
c^2 = a^2 + b^2 - 2*a*b*cos(C)
Substituting the given values into the formula:
c^2 = 22^2 + 8.5^2 - 2*22*8.5*cos(21)
Now we can calculate side C:
c = sqrt(22^2 + 8.5^2 - 2*22*8.5*cos(21))
= sqrt(484 + 72.25 - 37.4*0.92718)
= sqrt(484 + 72.25 - 34.63357)
= sqrt(521.61643)
≈ 22.84 cm (rounded to two decimal places)
Therefore, the length of side C is approximately 22.84 cm.