Given ABC with a = 6, b = 18, and mC 88° , find c. Round the cosine value to the nearest thousandth and answer to the nearest hundredth.
Now I got 28.32
c^2 = a^2 + b^2 - 2 a b cos C
88 is very close to 90 so approximately
c^2 = 36 + 324 = 360
c = about 19 so not 28.whatever
To find the length of side c in triangle ABC, we can use the Law of Cosines.
The Law of Cosines states that in any triangle ABC 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)
In this case, we are given:
a = 6 (length of side a)
b = 18 (length of side b)
mC = 88° (measure of angle C)
Let's substitute these values into the Law of Cosines equation and solve for c:
c^2 = 6^2 + 18^2 - 2*6*18 * cos(88°)
c^2 = 36 + 324 - 216 * cos(88°)
c^2 = 360 - 216 * cos(88°)
Now we need to calculate the cosine of 88°. To do this, we can use a scientific calculator or a calculator with trigonometric functions.
cos(88°) ≈ 0.0348994967 (rounded to the nearest ten-thousandth)
Now we can substitute this value back into the equation:
c^2 = 360 - 216 * 0.0348994967
c^2 ≈ 360 - 7.54981529012
c^2 ≈ 352.45018471
Taking the square root of both sides to isolate c, we get:
c ≈ √(352.45018471)
c ≈ 18.77
Therefore, the length of side c is approximately 18.77.